{"id":11214,"date":"2015-07-14T18:52:40","date_gmt":"2015-07-14T18:52:40","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&#038;p=11214"},"modified":"2015-09-09T21:15:04","modified_gmt":"2015-09-09T21:15:04","slug":"key-terms-glossary-8","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/key-terms-glossary-8\/","title":{"raw":"Key Terms &amp; Glossary","rendered":"Key Terms &amp; Glossary"},"content":{"raw":"<section id=\"fs-id1165135570408\" class=\"key-equations\" data-depth=\"1\">\r\n<h1 data-type=\"title\">Key Equations<\/h1>\r\n<table id=\"fs-id2922999\" summary=\"...\">\r\n<tbody>\r\n<tr>\r\n<td>The Product Rule for Logarithms<\/td>\r\n<td>[latex]{\\mathrm{log}}_{b}\\left(MN\\right)={\\mathrm{log}}_{b}\\left(M\\right)+{\\mathrm{log}}_{b}\\left(N\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The Quotient Rule for Logarithms<\/td>\r\n<td>[latex]{\\mathrm{log}}_{b}\\left(\\frac{M}{N}\\right)={\\mathrm{log}}_{b}M-{\\mathrm{log}}_{b}N[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The Power Rule for Logarithms<\/td>\r\n<td>[latex]{\\mathrm{log}}_{b}\\left({M}^{n}\\right)=n{\\mathrm{log}}_{b}M[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The Change-of-Base Formula<\/td>\r\n<td>[latex]{\\mathrm{log}}_{b}M\\text{=}\\frac{{\\mathrm{log}}_{n}M}{{\\mathrm{log}}_{n}b}\\text{ }n&gt;0,n\\ne 1,b\\ne 1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><section id=\"fs-id1165134049414\" class=\"key-concepts\" data-depth=\"1\">\r\n<h1 data-type=\"title\">Key Concepts<\/h1>\r\n<ul id=\"fs-id1165134049421\">\r\n\t<li>We can use the product rule of logarithms to rewrite the log of a product as a sum of logarithms.<\/li>\r\n\t<li>We can use the quotient rule of logarithms to rewrite the log of a quotient as a difference of logarithms.<\/li>\r\n\t<li>We can use the power rule for logarithms to rewrite the log of a power as the product of the exponent and the log of its base.<\/li>\r\n\t<li>We can use the product rule, the quotient rule, and the power rule together to combine or expand a logarithm with a complex input.<\/li>\r\n\t<li>The rules of logarithms can also be used to condense sums, differences, and products with the same base as a single logarithm.<\/li>\r\n\t<li>We can convert a logarithm with any base to a quotient of logarithms with any other base using the change-of-base formula.<\/li>\r\n\t<li>The change-of-base formula is often used to rewrite a logarithm with a base other than 10 and <i>e<\/i>\u00a0as the quotient of natural or common logs. That way a calculator can be used to evaluate.<\/li>\r\n<\/ul>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1165137890644\" class=\"definition\"><dt><strong>change-of-base formula<\/strong><\/dt><dd id=\"fs-id1165137890649\">a formula for converting a logarithm with any base to a quotient of logarithms with any other base.<\/dd><\/dl><dl id=\"fs-id1165137890654\" class=\"definition\"><dt><strong>power rule for logarithms<\/strong><\/dt><dd id=\"fs-id1165137890659\">a rule of logarithms that states that the log of a power is equal to the product of the exponent and the log of its base<\/dd><\/dl><dl id=\"fs-id1165137890664\" class=\"definition\"><dt><strong>product rule for logarithms<\/strong><\/dt><dd id=\"fs-id1165137890670\">a rule of logarithms that states that the log of a product is equal to a sum of logarithms<\/dd><\/dl><dl id=\"fs-id1165137890674\" class=\"definition\"><dt><strong>quotient rule for logarithms<\/strong><\/dt><dd id=\"fs-id1165137890679\">a rule of logarithms that states that the log of a quotient is equal to a difference of logarithms<\/dd><\/dl><\/section>","rendered":"<section id=\"fs-id1165135570408\" class=\"key-equations\" data-depth=\"1\">\n<h1 data-type=\"title\">Key Equations<\/h1>\n<table id=\"fs-id2922999\" summary=\"...\">\n<tbody>\n<tr>\n<td>The Product Rule for Logarithms<\/td>\n<td>[latex]{\\mathrm{log}}_{b}\\left(MN\\right)={\\mathrm{log}}_{b}\\left(M\\right)+{\\mathrm{log}}_{b}\\left(N\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The Quotient Rule for Logarithms<\/td>\n<td>[latex]{\\mathrm{log}}_{b}\\left(\\frac{M}{N}\\right)={\\mathrm{log}}_{b}M-{\\mathrm{log}}_{b}N[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The Power Rule for Logarithms<\/td>\n<td>[latex]{\\mathrm{log}}_{b}\\left({M}^{n}\\right)=n{\\mathrm{log}}_{b}M[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The Change-of-Base Formula<\/td>\n<td>[latex]{\\mathrm{log}}_{b}M\\text{=}\\frac{{\\mathrm{log}}_{n}M}{{\\mathrm{log}}_{n}b}\\text{ }n>0,n\\ne 1,b\\ne 1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165134049414\" class=\"key-concepts\" data-depth=\"1\">\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1165134049421\">\n<li>We can use the product rule of logarithms to rewrite the log of a product as a sum of logarithms.<\/li>\n<li>We can use the quotient rule of logarithms to rewrite the log of a quotient as a difference of logarithms.<\/li>\n<li>We can use the power rule for logarithms to rewrite the log of a power as the product of the exponent and the log of its base.<\/li>\n<li>We can use the product rule, the quotient rule, and the power rule together to combine or expand a logarithm with a complex input.<\/li>\n<li>The rules of logarithms can also be used to condense sums, differences, and products with the same base as a single logarithm.<\/li>\n<li>We can convert a logarithm with any base to a quotient of logarithms with any other base using the change-of-base formula.<\/li>\n<li>The change-of-base formula is often used to rewrite a logarithm with a base other than 10 and <i>e<\/i>\u00a0as the quotient of natural or common logs. That way a calculator can be used to evaluate.<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137890644\" class=\"definition\">\n<dt><strong>change-of-base formula<\/strong><\/dt>\n<dd id=\"fs-id1165137890649\">a formula for converting a logarithm with any base to a quotient of logarithms with any other base.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137890654\" class=\"definition\">\n<dt><strong>power rule for logarithms<\/strong><\/dt>\n<dd id=\"fs-id1165137890659\">a rule of logarithms that states that the log of a power is equal to the product of the exponent and the log of its base<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137890664\" class=\"definition\">\n<dt><strong>product rule for logarithms<\/strong><\/dt>\n<dd id=\"fs-id1165137890670\">a rule of logarithms that states that the log of a product is equal to a sum of logarithms<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137890674\" class=\"definition\">\n<dt><strong>quotient rule for logarithms<\/strong><\/dt>\n<dd id=\"fs-id1165137890679\">a rule of logarithms that states that the log of a quotient is equal to a difference of logarithms<\/dd>\n<\/dl>\n<\/section>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-11214\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-11214","chapter","type-chapter","status-publish","hentry"],"part":11201,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11214","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11214\/revisions"}],"predecessor-version":[{"id":12992,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11214\/revisions\/12992"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/parts\/11201"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/11214\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/media?parent=11214"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapter-type?post=11214"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/contributor?post=11214"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/license?post=11214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}