{"id":280,"date":"2023-06-21T13:22:51","date_gmt":"2023-06-21T13:22:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-13\/"},"modified":"2023-07-03T21:04:45","modified_gmt":"2023-07-03T21:04:45","slug":"summary-review-13","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-13\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>Logarithms have properties similar to exponential properties because logarithms and exponents are of inverse forms to one another.<\/li>\n \t<li>Use the inverse nature and the definition of the logarithm to prove the properties of logarithms.<\/li>\n \t<li>Recall that exponents are added when like bases are multiplied as a reminder that the logarithm of a product is equivalent to a sum of logarithms to the same base.<\/li>\n \t<li>Recall that exponents are subtracted when like bases are divided as a reminder that the logarithm of a quotient is equivalent to a difference of logarithms to the same base.<\/li>\n<\/ul>\n<h2>Key Equations<\/h2>\n<ul>\n \t<li>[latex]\\log_bx=y \\ \\Leftrightarrow \\ b^y=x[\/latex]<\/li>\n \t<li>[latex]\\log_b\\left(MN\\right)=\\log_b\\left(M\\right) + \\log_b\\left(N\\right)[\/latex]<\/li>\n \t<li>[latex]\\log_b\\left(\\dfrac{M}{N}\\right)=\\log_b\\left(M\\right) - \\log_b\\left(N\\right)[\/latex]<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n \t<dt><strong>one-to-one property of exponents<\/strong><\/dt>\n \t<dd>states that [latex]a^m=a^n \\Leftrightarrow m=n[\/latex]<\/dd>\n \t<dt><strong>one-to-one property of logarithms <\/strong><\/dt>\n \t<dd>states that [latex]\\log_b\\left(M\\right)=\\log_b\\left(N\\right) \\Leftrightarrow M=N[\/latex]<\/dd>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Logarithms have properties similar to exponential properties because logarithms and exponents are of inverse forms to one another.<\/li>\n<li>Use the inverse nature and the definition of the logarithm to prove the properties of logarithms.<\/li>\n<li>Recall that exponents are added when like bases are multiplied as a reminder that the logarithm of a product is equivalent to a sum of logarithms to the same base.<\/li>\n<li>Recall that exponents are subtracted when like bases are divided as a reminder that the logarithm of a quotient is equivalent to a difference of logarithms to the same base.<\/li>\n<\/ul>\n<h2>Key Equations<\/h2>\n<ul>\n<li>[latex]\\log_bx=y \\ \\Leftrightarrow \\ b^y=x[\/latex]<\/li>\n<li>[latex]\\log_b\\left(MN\\right)=\\log_b\\left(M\\right) + \\log_b\\left(N\\right)[\/latex]<\/li>\n<li>[latex]\\log_b\\left(\\dfrac{M}{N}\\right)=\\log_b\\left(M\\right) - \\log_b\\left(N\\right)[\/latex]<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>one-to-one property of exponents<\/strong><\/dt>\n<dd>states that [latex]a^m=a^n \\Leftrightarrow m=n[\/latex]<\/dd>\n<dt><strong>one-to-one property of logarithms <\/strong><\/dt>\n<dd>states that [latex]\\log_b\\left(M\\right)=\\log_b\\left(N\\right) \\Leftrightarrow M=N[\/latex]<\/dd>\n<\/dl>\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-280\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/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":395986,"menu_order":41,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-280","chapter","type-chapter","status-publish","hentry"],"part":251,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/280\/revisions"}],"predecessor-version":[{"id":647,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/280\/revisions\/647"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/251"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/280\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=280"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=280"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=280"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}