{"id":5540,"date":"2022-09-21T16:37:32","date_gmt":"2022-09-21T16:37:32","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5540"},"modified":"2022-10-17T16:47:14","modified_gmt":"2022-10-17T16:47:14","slug":"16d-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/16d-preview\/","title":{"raw":"16D Preview","rendered":"16D Preview"},"content":{"raw":"
\r\n
Preparing for the next classIn the next in-class activity, you will need to be able to evaluate mathematical expressions by squaring numbers, taking the square root of numbers, and taking the logarithms of numbers. You will also need to describe trends in what happens to numbers when you square them, take their square roots, and take their logarithms.<\/div>\r\n
Questions 1\u20135: We need to explore what happens when we square a number (raise it to the second power). For example, when we square the number 5, we get 52=5\u22c55=25<\/div>\r\n
\r\n
\r\n

Question 1<\/h3>\r\n1) For each number in the table, calculate the square of that number. You may use a calculator.\r\n\r\n\r\n\r\n\r\n
Original number<\/strong><\/td>\r\n1293<\/td>\r\n5<\/td>\r\n0<\/td>\r\n0.4<\/td>\r\n1<\/td>\r\n4.76<\/td>\r\n33<\/td>\r\n492.1<\/td>\r\n2084<\/td>\r\n<\/tr>\r\n
Number squared<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 2<\/h3>\r\n
2) If you were to order the list of squared numbers from least to greatest, would it be in the same order as the original list of numbers?<\/div>\r\n
a) Yes<\/div>\r\n
b) No<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 3<\/h3>\r\n
3) Compare the numbers 4.76 and 2084. Which is greater\u2014the distance between 4.76 and 2084 or the distance between 4.762 and 20842?<\/div>\r\n
a)The distance between 4.76 and 2938<\/div>\r\n
b) The distance between 4.762 and 20842<\/div>\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
Go to the website https:\/\/www.desmos.com\/calculator. To continue exploring how to square quantities, we will graph the line \ud835\udc66=\ud835\udc65along with the graph of \ud835\udc66=\ud835\udc652.<\/div>\r\n
On the left-hand side of the screen, enter the equations \ud835\udc66=\ud835\udc65and\ud835\udc66=\ud835\udc652, as shown below. To write \u201c\ud835\udc652,\u201d type \u201cx^2\u201d on your keyboard.<\/div>\r\n
\"The<\/div>\r\n
This will show the graphs of both equations.<\/div>\r\n
\r\n
\r\n

Question 4<\/h3>\r\n
4) For values of \ud835\udc65greater than 1, what happens to the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652as \ud835\udc65gets larger (in other words, as we move to the right along the \ud835\udc65-axis)?<\/div>\r\n
a)As \ud835\udc65gets larger, the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652stays the same.<\/div>\r\n
b)As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652gets larger.<\/div>\r\n
c)As \ud835\udc65gets larger, the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652gets smaller.<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 5<\/h3>\r\n
5) Based on your answers to the questions about squaring numbers, which of the following is true?<\/div>\r\n
a) For numbers greater than 1, squaring small numbers makes them a lot bigger and squaring big numbers makes them a little bigger.<\/div>\r\n
b) For numbers greater than 1, squaring small numbers makes them a little bigger and squaring big numbers makes them a lot bigger.<\/div>\r\n
c) For numbers greater than 1, squaring small numbers makes them a lot smaller and squaring big numbers makes them a little smaller.<\/div>\r\n
d) For numbers greater than 1, squaring small numbers makes them a little smaller and squaring big numbers makes them a lot smaller.<\/div>\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
Questions 6\u201310: Next, we will explore what happens when we take the square root of a number. A square root of a number is a value that, when multiplied by itself, gives the number.[footnote]Definition of square root. (n.d.). Mathisfun.com. https:\/\/www.mathsisfun.com\/definitions\/square-root.html[\/footnote] For example, 9 has two square roots: 3 and \u22123. When we use the symbol \u221a, however, we mean the positive square root. Therefore, \u221a9=3because 3\u22c53 =9.<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 6<\/h3>\r\n6) For each number in the table, calculate the positive square root of that number. You may use a calculator. If necessary, round to three decimal places. If a value is undefined, write \u201cUND.\u201d\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Original number<\/strong><\/td>\r\nPositive square root of number<\/strong><\/td>\r\n<\/tr>\r\n
1293<\/td>\r\n<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n<\/td>\r\n<\/tr>\r\n
0<\/td>\r\n<\/td>\r\n<\/tr>\r\n
0.4<\/td>\r\n<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n<\/td>\r\n<\/tr>\r\n
4.76<\/td>\r\n<\/td>\r\n<\/tr>\r\n
33<\/td>\r\n<\/td>\r\n<\/tr>\r\n
492.1<\/td>\r\n<\/td>\r\n<\/tr>\r\n
2084<\/td>\r\n <\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nOn https:\/\/www.desmos.com\/calculator, enter the equations \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65, as shown in the following graphic. For\u201c\u221a\ud835\udc65,\u201d type \u201csqrtx\u201d on your keyboard.\r\n\r\n\"The\r\n\r\n<\/div>\r\n
\r\n
\r\n

Question 7<\/h3>\r\n
7) Based on the graph of \ud835\udc66=\u221a\ud835\udc65and on the table in Question 6, what values of \ud835\udc65can you take the square root of?<\/div>\r\n
a) All real numbers<\/div>\r\n
b) \ud835\udc65<0c)\ud835\udc65\u22650<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 8<\/h3>\r\n
8) Compare the numbers 4.76 and 2084. Which is greater\u2014the distance between 4.76 and 2084or the distance between \u221a4.76and \u221a2084?<\/div>\r\n
a) The distance between 4.76 and 2084<\/div>\r\n
b) The distance between \u221a4.76and \u221a2084<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 9<\/h3>\r\n
9) For values of \ud835\udc65greater than 1, what happens to the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65as \ud835\udc65gets larger (in other words, as we move to the right along the \ud835\udc65-axis)?<\/div>\r\n
a) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65stays the same.<\/div>\r\n
b) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65gets larger.<\/div>\r\n
c) As \ud835\udc65gets larger, the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65gets smaller.<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 10<\/h3>\r\n
10) Based on your answers to questions about taking the square root of a number, which of the following is true?<\/div>\r\n
a) For numbers greater than 1, taking the square roots of small numbers makes them a lot bigger and taking the square rootsof big numbers makes them a little bigger.<\/div>\r\n
b) For numbers greater than 1, taking the square rootsof small numbers makes them a little bigger and taking the square rootsof big numbers makes them a lot bigger.<\/div>\r\n
c) For numbers greater than 1, taking the square rootsof small numbers makes them a lot smaller and taking the square rootsof big numbers makes them a little smaller.<\/div>\r\n
d) For numbers greater than 1, taking the square rootsof small numbers makes them a little smaller and taking the square rootsof big numbers makes them a lot smaller.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
Questions 11\u201315: Finally, we will explore what happens when we take the logarithm of a number. A logarithm answers the question, \u201cTo what power must we raise one number to get another number?\u201d For example, consider the question,\u201cTo what power must we raise 2 to get 8?\u201d We see that<\/span><\/div>\r\n<\/div>\r\n
\r\n
2 \u22192 \u22192 =23<\/sup>=8<\/div>\r\n
So, the answer to our question is 3. The way we write this logarithm is<\/div>\r\n
log2<\/sub>(8)= 3<\/div>\r\n
and in fact, the statements<\/div>\r\n
23<\/sup>=8and log2<\/sub>(8)=3<\/div>\r\n
contain the same information. In general, the statements<\/div>\r\n
\ud835\udc4f\ud835\udc65<\/sup>=\ud835\udc4e and log\ud835\udc4f<\/sub>(\ud835\udc4e)=\ud835\udc65<\/div>\r\n
contain the same information. In both the exponential form and the logarithmic form, the quantity \ud835\udc4fis called the base. A base that is often used in logarithms is 10; instead of writing log10<\/sub>(\ud835\udc4e), we often just write log(\ud835\udc4e).Another common base that you may encounter is the irrational number \ud835\udc52, which is approximately equal to 2.718; instead of writing log\ud835\udc52<\/sub>(\ud835\udc4e), we often just write ln(\ud835\udc4e)and call this the \u201cnatural logarithm of \ud835\udc4e.\u201d<\/div>\r\n
\r\n
\r\n

Question 11<\/h3>\r\n11) For each number in the following table, calculate the base10 logarithm of that number. (On a calculator, use the button labeled \u201clog\u201d or \u201cLOG.\u201d) If necessary, round to three decimal places. If a value is undefined, write \u201cUND.\u201d\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Original number<\/td>\r\nBase 10 logarithm<\/td>\r\n<\/tr>\r\n
1293<\/td>\r\n<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n<\/td>\r\n<\/tr>\r\n
0<\/td>\r\n<\/td>\r\n<\/tr>\r\n
0.4<\/td>\r\n<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n<\/td>\r\n<\/tr>\r\n
4.76<\/td>\r\n<\/td>\r\n<\/tr>\r\n
33<\/td>\r\n<\/td>\r\n<\/tr>\r\n
492.1<\/td>\r\n<\/td>\r\n<\/tr>\r\n
2084<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nOn https:\/\/www.desmos.com\/calculator, enter the equations \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65), as shown in the following graphic.\r\n\r\n\"The\r\n\r\n<\/div>\r\n
\r\n
\r\n

Question 12<\/h3>\r\n
12) Based on the graph of \ud835\udc66=log(x)and on the table in Question 11, what values of \ud835\udc65can you take the base 10 logarithm of?<\/div>\r\n
a) All real numbers<\/div>\r\n
b) \ud835\udc65\u22640<\/div>\r\n
c) \ud835\udc65>0<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 13<\/h3>\r\n
13) Compare the numbers 4.76 and 2084. Which is greater\u2014the distance between 4.76 and 2084or the distance between log(4.76) and log(2084)?<\/div>\r\n
a) The distance between 4.76 and 2084<\/div>\r\n
b) The distance between log(4.76)and log(2084)<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 14<\/h3>\r\n
14) For values of \ud835\udc65greater than 1, what happens to the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)as \ud835\udc65gets larger (in other words, as we move to the right along the \ud835\udc65-axis)?<\/div>\r\n
a) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)stays the same.<\/div>\r\n
b) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)gets larger.<\/div>\r\n
c) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)gets smaller.<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 15<\/h3>\r\n
15) Based on your answers to the previous two questions, which of the following is true?<\/div>\r\n
a) For numbers greater than 1, taking the base10 logarithm of small numbers makes them a lot bigger and taking the base10 logarithm of big numbers makes them a little bigger.<\/div>\r\n
b) For numbers greater than 1, taking the base10logarithm of small numbers makes them a little bigger and taking the base10 logarithm of big numbers makes them a lot bigger.<\/div>\r\n
c) For numbers greater than 1, taking the base10 logarithm of small numbers makes them a lot smaller and taking the base10 logarithm of big numbers makes them a little smaller.<\/div>\r\n
d) For numbers greater than 1, taking the base10 logarithm of small numbers makes them a little smaller and taking the base10 logarithm of big numbers makes them a lot smaller.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
Preparing for the next classIn the next in-class activity, you will need to be able to evaluate mathematical expressions by squaring numbers, taking the square root of numbers, and taking the logarithms of numbers. You will also need to describe trends in what happens to numbers when you square them, take their square roots, and take their logarithms.<\/div>\n
Questions 1\u20135: We need to explore what happens when we square a number (raise it to the second power). For example, when we square the number 5, we get 52=5\u22c55=25<\/div>\n
\n
\n

Question 1<\/h3>\n

1) For each number in the table, calculate the square of that number. You may use a calculator.<\/p>\n\n\n\n\n
Original number<\/strong><\/td>\n1293<\/td>\n5<\/td>\n0<\/td>\n0.4<\/td>\n1<\/td>\n4.76<\/td>\n33<\/td>\n492.1<\/td>\n2084<\/td>\n<\/tr>\n
Number squared<\/strong><\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Question 2<\/h3>\n
2) If you were to order the list of squared numbers from least to greatest, would it be in the same order as the original list of numbers?<\/div>\n
a) Yes<\/div>\n
b) No<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 3<\/h3>\n
3) Compare the numbers 4.76 and 2084. Which is greater\u2014the distance between 4.76 and 2084 or the distance between 4.762 and 20842?<\/div>\n
a)The distance between 4.76 and 2938<\/div>\n
b) The distance between 4.762 and 20842<\/div>\n<\/div>\n<\/div>\n
<\/div>\n
Go to the website https:\/\/www.desmos.com\/calculator. To continue exploring how to square quantities, we will graph the line \ud835\udc66=\ud835\udc65along with the graph of \ud835\udc66=\ud835\udc652.<\/div>\n
On the left-hand side of the screen, enter the equations \ud835\udc66=\ud835\udc65and\ud835\udc66=\ud835\udc652, as shown below. To write \u201c\ud835\udc652,\u201d type \u201cx^2\u201d on your keyboard.<\/div>\n
\"The<\/div>\n
This will show the graphs of both equations.<\/div>\n
\n
\n

Question 4<\/h3>\n
4) For values of \ud835\udc65greater than 1, what happens to the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652as \ud835\udc65gets larger (in other words, as we move to the right along the \ud835\udc65-axis)?<\/div>\n
a)As \ud835\udc65gets larger, the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652stays the same.<\/div>\n
b)As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652gets larger.<\/div>\n
c)As \ud835\udc65gets larger, the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\ud835\udc652gets smaller.<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 5<\/h3>\n
5) Based on your answers to the questions about squaring numbers, which of the following is true?<\/div>\n
a) For numbers greater than 1, squaring small numbers makes them a lot bigger and squaring big numbers makes them a little bigger.<\/div>\n
b) For numbers greater than 1, squaring small numbers makes them a little bigger and squaring big numbers makes them a lot bigger.<\/div>\n
c) For numbers greater than 1, squaring small numbers makes them a lot smaller and squaring big numbers makes them a little smaller.<\/div>\n
d) For numbers greater than 1, squaring small numbers makes them a little smaller and squaring big numbers makes them a lot smaller.<\/div>\n<\/div>\n<\/div>\n
<\/div>\n
Questions 6\u201310: Next, we will explore what happens when we take the square root of a number. A square root of a number is a value that, when multiplied by itself, gives the number.[1]<\/sup><\/a> For example, 9 has two square roots: 3 and \u22123. When we use the symbol \u221a, however, we mean the positive square root. Therefore, \u221a9=3because 3\u22c53 =9.<\/div>\n
<\/div>\n
\n
\n

Question 6<\/h3>\n

6) For each number in the table, calculate the positive square root of that number. You may use a calculator. If necessary, round to three decimal places. If a value is undefined, write \u201cUND.\u201d<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
Original number<\/strong><\/td>\nPositive square root of number<\/strong><\/td>\n<\/tr>\n
1293<\/td>\n<\/td>\n<\/tr>\n
5<\/td>\n<\/td>\n<\/tr>\n
0<\/td>\n<\/td>\n<\/tr>\n
0.4<\/td>\n<\/td>\n<\/tr>\n
1<\/td>\n<\/td>\n<\/tr>\n
4.76<\/td>\n<\/td>\n<\/tr>\n
33<\/td>\n<\/td>\n<\/tr>\n
492.1<\/td>\n<\/td>\n<\/tr>\n
2084<\/td>\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

On https:\/\/www.desmos.com\/calculator, enter the equations \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65, as shown in the following graphic. For\u201c\u221a\ud835\udc65,\u201d type \u201csqrtx\u201d on your keyboard.<\/p>\n

\"The<\/p>\n<\/div>\n

\n
\n

Question 7<\/h3>\n
7) Based on the graph of \ud835\udc66=\u221a\ud835\udc65and on the table in Question 6, what values of \ud835\udc65can you take the square root of?<\/div>\n
a) All real numbers<\/div>\n
b) \ud835\udc65<0c)\ud835\udc65\u22650<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 8<\/h3>\n
8) Compare the numbers 4.76 and 2084. Which is greater\u2014the distance between 4.76 and 2084or the distance between \u221a4.76and \u221a2084?<\/div>\n
a) The distance between 4.76 and 2084<\/div>\n
b) The distance between \u221a4.76and \u221a2084<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 9<\/h3>\n
9) For values of \ud835\udc65greater than 1, what happens to the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65as \ud835\udc65gets larger (in other words, as we move to the right along the \ud835\udc65-axis)?<\/div>\n
a) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65stays the same.<\/div>\n
b) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65gets larger.<\/div>\n
c) As \ud835\udc65gets larger, the distance between the graphsof \ud835\udc66=\ud835\udc65and \ud835\udc66=\u221a\ud835\udc65gets smaller.<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 10<\/h3>\n
10) Based on your answers to questions about taking the square root of a number, which of the following is true?<\/div>\n
a) For numbers greater than 1, taking the square roots of small numbers makes them a lot bigger and taking the square rootsof big numbers makes them a little bigger.<\/div>\n
b) For numbers greater than 1, taking the square rootsof small numbers makes them a little bigger and taking the square rootsof big numbers makes them a lot bigger.<\/div>\n
c) For numbers greater than 1, taking the square rootsof small numbers makes them a lot smaller and taking the square rootsof big numbers makes them a little smaller.<\/div>\n
d) For numbers greater than 1, taking the square rootsof small numbers makes them a little smaller and taking the square rootsof big numbers makes them a lot smaller.<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
Questions 11\u201315: Finally, we will explore what happens when we take the logarithm of a number. A logarithm answers the question, \u201cTo what power must we raise one number to get another number?\u201d For example, consider the question,\u201cTo what power must we raise 2 to get 8?\u201d We see that<\/span><\/div>\n<\/div>\n
\n
2 \u22192 \u22192 =23<\/sup>=8<\/div>\n
So, the answer to our question is 3. The way we write this logarithm is<\/div>\n
log2<\/sub>(8)= 3<\/div>\n
and in fact, the statements<\/div>\n
23<\/sup>=8and log2<\/sub>(8)=3<\/div>\n
contain the same information. In general, the statements<\/div>\n
\ud835\udc4f\ud835\udc65<\/sup>=\ud835\udc4e and log\ud835\udc4f<\/sub>(\ud835\udc4e)=\ud835\udc65<\/div>\n
contain the same information. In both the exponential form and the logarithmic form, the quantity \ud835\udc4fis called the base. A base that is often used in logarithms is 10; instead of writing log10<\/sub>(\ud835\udc4e), we often just write log(\ud835\udc4e).Another common base that you may encounter is the irrational number \ud835\udc52, which is approximately equal to 2.718; instead of writing log\ud835\udc52<\/sub>(\ud835\udc4e), we often just write ln(\ud835\udc4e)and call this the \u201cnatural logarithm of \ud835\udc4e.\u201d<\/div>\n
\n
\n

Question 11<\/h3>\n

11) For each number in the following table, calculate the base10 logarithm of that number. (On a calculator, use the button labeled \u201clog\u201d or \u201cLOG.\u201d) If necessary, round to three decimal places. If a value is undefined, write \u201cUND.\u201d<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
Original number<\/td>\nBase 10 logarithm<\/td>\n<\/tr>\n
1293<\/td>\n<\/td>\n<\/tr>\n
5<\/td>\n<\/td>\n<\/tr>\n
0<\/td>\n<\/td>\n<\/tr>\n
0.4<\/td>\n<\/td>\n<\/tr>\n
1<\/td>\n<\/td>\n<\/tr>\n
4.76<\/td>\n<\/td>\n<\/tr>\n
33<\/td>\n<\/td>\n<\/tr>\n
492.1<\/td>\n<\/td>\n<\/tr>\n
2084<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

On https:\/\/www.desmos.com\/calculator, enter the equations \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65), as shown in the following graphic.<\/p>\n

\"The<\/p>\n<\/div>\n

\n
\n

Question 12<\/h3>\n
12) Based on the graph of \ud835\udc66=log(x)and on the table in Question 11, what values of \ud835\udc65can you take the base 10 logarithm of?<\/div>\n
a) All real numbers<\/div>\n
b) \ud835\udc65\u22640<\/div>\n
c) \ud835\udc65>0<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 13<\/h3>\n
13) Compare the numbers 4.76 and 2084. Which is greater\u2014the distance between 4.76 and 2084or the distance between log(4.76) and log(2084)?<\/div>\n
a) The distance between 4.76 and 2084<\/div>\n
b) The distance between log(4.76)and log(2084)<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 14<\/h3>\n
14) For values of \ud835\udc65greater than 1, what happens to the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)as \ud835\udc65gets larger (in other words, as we move to the right along the \ud835\udc65-axis)?<\/div>\n
a) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)stays the same.<\/div>\n
b) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)gets larger.<\/div>\n
c) As \ud835\udc65gets larger, the distance between the graphs of \ud835\udc66=\ud835\udc65and \ud835\udc66=log(\ud835\udc65)gets smaller.<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 15<\/h3>\n
15) Based on your answers to the previous two questions, which of the following is true?<\/div>\n
a) For numbers greater than 1, taking the base10 logarithm of small numbers makes them a lot bigger and taking the base10 logarithm of big numbers makes them a little bigger.<\/div>\n
b) For numbers greater than 1, taking the base10logarithm of small numbers makes them a little bigger and taking the base10 logarithm of big numbers makes them a lot bigger.<\/div>\n
c) For numbers greater than 1, taking the base10 logarithm of small numbers makes them a lot smaller and taking the base10 logarithm of big numbers makes them a little smaller.<\/div>\n
d) For numbers greater than 1, taking the base10 logarithm of small numbers makes them a little smaller and taking the base10 logarithm of big numbers makes them a lot smaller.<\/div>\n<\/div>\n<\/div>\n<\/div>\n
  1. Definition of square root. (n.d.). Mathisfun.com. https:\/\/www.mathsisfun.com\/definitions\/square-root.html ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"menu_order":68,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5540","chapter","type-chapter","status-publish","hentry"],"part":5514,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5540","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5540\/revisions"}],"predecessor-version":[{"id":5646,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5540\/revisions\/5646"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5514"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5540\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5540"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5540"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5540"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5540"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}