neve domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home/mathze5/public_html/learnermath.com/wp-includes/functions.php on line 6114The exponential and logarithmic functions<\/i><\/a> introduction page focused on both types of functions and the relationship between them.\n On this Page: 1. Exponential and Log Examples 2. Further Examples The exponential and logarithmic functions introduction page focused on both types of functions and the relationship between them. Here we will look at some of the types of exponential and logarithmic functions examples and problems that can be encountered, and how they can be… Read More »Exponential and Logarithmic Functions
\nHere we will look at some of the types of exponential and logarithmic functions examples and problems that can be encountered, and how they can be solved.<\/p>\n
\n<\/a>\n
\nExamples <\/font><\/font><\/font><\/u><\/b>\n
\n(1.1) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWrite {\\tt{log}}_4 (64) \\space {\\small{=}} \\space 3<\/span><\/font> in exponential form.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n{\\tt{log}}_4 (64) \\space {\\small{=}} \\space 3<\/span><\/font> => 4^3 \\space {\\small{=}} \\space 64<\/span><\/font>\n
\n(1.2) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWrite 2^4 \\space {\\small{=}} \\space 16<\/span><\/font> in exponential form.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n2^4 \\space {\\small{=}} \\space 16<\/span><\/font> => {\\tt{log}}_2 (16) \\space {\\small{=}} \\space 4<\/span><\/font>\n
\n(1.3) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nExpress 5^2 \\space {\\small{=}} \\space t<\/span><\/font> in logarithmic form.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n5^2 \\space {\\small{=}} \\space t<\/span><\/font> => {\\tt{log}}_5 (t) \\space {\\small{=}} \\space 2<\/span><\/font>\n
\n(1.4) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWhat value is t<\/i><\/font> where {\\tt{log}}_5 (t) \\space {\\small{=}} \\space 3<\/span> ?<\/font>\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n{\\tt{log}}_5 (t) \\space {\\small{=}} \\space 3<\/span><\/font> => 5^3 \\space {\\small{=}} \\space t<\/span><\/font> => 125 \\space {\\small{=}} \\space t<\/span><\/font>\n
\n(1.5) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nEvaluate {\\tt{log}}_a (\\frac{1}{32}) \\space {\\small{=}} \\space {\\text{-}}5<\/span><\/font>.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u>\n
\na^{{\\text{-}}5} \\space {\\small{=}} \\space \\frac{1}{32}<\/span><\/font> => \\frac{1}{a^5} \\space {\\small{=}} \\space \\frac{1}{32}<\/span><\/font> => a \\space {\\small{=}} \\space 2<\/span><\/font>\n
\n
\n<\/a>\n
\n\n\n\n
\n\n\n\nExponential and Logarithmic Functions
Examples, Further<\/span><\/h2>\n\n\n\n
\n(2.1) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nSolve for x<\/span> where {\\tt{log}}_x (9) \\space {\\small{=}} \\space 4<\/span><\/font>.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n{\\tt{log}}_x (9) \\space {\\small{=}} \\space 4<\/span><\/font> => x^4 \\space {\\small{=}} \\space 9<\/span><\/font>\n
\nx^4 \\space {\\small{=}} \\space 9<\/span><\/font>\n
\n(x^2)^2 \\space {\\small{=}} \\space 9<\/span><\/font>\n
\nx^2 \\space {\\small{=}} \\space 3<\/span><\/font> , x \\space {\\small{=}} \\space \\sqrt{3}<\/span><\/font>\n
\n(2.2) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nSolve for r<\/span> where {\\tt{log}}_{625} (5) \\space {\\small{=}} \\space r<\/span><\/font>.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n{\\tt{log}}_{625} (5) \\space {\\small{=}} \\space r<\/span><\/font> => 625^r \\space {\\small{=}} \\space 5<\/span><\/font>\n
\nAt this point, it helps to know that<\/font>,\n
\n{\\tt{log}}_5 (625) \\space {\\small{=}} \\space 4<\/span><\/font> => 5^4 \\space {\\small{=}} \\space 625<\/span><\/font>.\n
\nSo we can write 625^r \\space {\\small{=}} \\space 5<\/span><\/font> as (5^4)^r \\space {\\small{=}} \\space 5<\/span><\/font>.\n
\nNow:\n
\n(5^4)^r \\space {\\small{=}} \\space 5^1<\/span><\/font> => 5^{4r} \\space {\\small{=}} \\space 5^1<\/span><\/font> => 4r \\space {\\small{=}} \\space 1<\/span><\/font> , r \\space {\\small{=}} \\space \\frac{1}{4}<\/span><\/font>\n
\n(2.3) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nSolve for p<\/span> where {\\tt{log}}_{0.5} (p) \\space {\\small{=}} \\space {\\text{-}}4<\/span><\/font>.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\n{\\tt{log}}_{0.5} (p) \\space {\\small{=}} \\space {\\text{-}}4<\/span><\/font> => 0.5^{{\\text{-}}4} \\space {\\small{=}} \\space p<\/span><\/font>\n
\n0.5^{{\\text{-}}4} \\space {\\small{=}} \\space p<\/span><\/font> => (\\frac{1}{2})^{{\\text{-}}4} \\space {\\small{=}} \\space p<\/span><\/font>\n
\nNow:\n
\n(\\frac{2}{1})^4 \\space {\\small{=}} \\space p<\/span><\/font> => 16 \\space {\\small{=}} \\space p<\/span><\/font>\n
\n
\n\n\n\n
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Examples<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"wf_page_folders":[18],"class_list":["post-1013","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages\/1013","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/comments?post=1013"}],"version-history":[{"count":9,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages\/1013\/revisions"}],"predecessor-version":[{"id":3653,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages\/1013\/revisions\/3653"}],"wp:attachment":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/media?parent=1013"}],"wp:term":[{"taxonomy":"wf_page_folders","embeddable":true,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/wf_page_folders?post=1013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}