{"id":270,"date":"2023-06-21T13:22:50","date_gmt":"2023-06-21T13:22:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/introduction-graphs-of-logarithmic-functions\/"},"modified":"2024-01-09T16:16:54","modified_gmt":"2024-01-09T16:16:54","slug":"introduction-graphs-of-logarithmic-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/introduction-graphs-of-logarithmic-functions\/","title":{"raw":"5.4b Introduction to Graphs of Logarithmic Functions","rendered":"5.4b Introduction to Graphs of Logarithmic Functions"},"content":{"raw":"

What you\u2019ll learn to do: Graph logarithmic functions and evaluate the results<\/h2>\r\nPreviously, we saw how creating a graphical representation of an exponential model gives us another layer of insight for predicting future events. How do logarithmic graphs give us insight into situations? Because every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation. In other words, logarithms give the cause<\/em> for an effect<\/em>.\r\n\r\nTo illustrate, suppose we invest $2500 in an account that offers an annual interest rate of 5% compounded continuously. We already know that the balance in our account for any year t<\/em>\u00a0can be found with the equation [latex]A=2500{e}^{0.05t}[\/latex].\r\n\r\nWhat if we wanted to know the year for any balance? We would need to create a corresponding new function by interchanging the input and the output; thus we would need to create a logarithmic model for this situation. By graphing the model, we can see the output (year) for any input (account balance). For instance, what if we wanted to know how many years it would take for our initial investment to double? The graph below shows this point.\r\n\r\n\"A\r\n\r\nIn this section we will discuss the values for which a logarithmic function is defined and then turn our attention to graphing the family of logarithmic functions.","rendered":"

What you\u2019ll learn to do: Graph logarithmic functions and evaluate the results<\/h2>\n

Previously, we saw how creating a graphical representation of an exponential model gives us another layer of insight for predicting future events. How do logarithmic graphs give us insight into situations? Because every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation. In other words, logarithms give the cause<\/em> for an effect<\/em>.<\/p>\n

To illustrate, suppose we invest $2500 in an account that offers an annual interest rate of 5% compounded continuously. We already know that the balance in our account for any year t<\/em>\u00a0can be found with the equation [latex]A=2500{e}^{0.05t}[\/latex].<\/p>\n

What if we wanted to know the year for any balance? We would need to create a corresponding new function by interchanging the input and the output; thus we would need to create a logarithmic model for this situation. By graphing the model, we can see the output (year) for any input (account balance). For instance, what if we wanted to know how many years it would take for our initial investment to double? The graph below shows this point.<\/p>\n

\"A<\/p>\n

In this section we will discuss the values for which a logarithmic function is defined and then turn our attention to graphing the family of logarithmic functions.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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