{"id":5653,"date":"2013-04-05T12:40:58","date_gmt":"2013-04-05T12:40:58","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=5653"},"modified":"2014-12-02T08:27:03","modified_gmt":"2014-12-02T08:27:03","slug":"exponential-and-logarithmic-functions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/exponential-and-logarithmic-functions\/","title":{"rendered":"Exponential and Logarithmic Functions"},"content":{"rendered":"<p><strong>Overview:\u00a0 What Are Exponential Functions?<\/strong><br \/>\nExponential functions are a special type of mathematical functions that follow the formula y = a<sup>x<\/sup>.\u00a0 The constant a and the exponent x are both real numbers.\u00a0 In addition, a is not equal to 1 and a &gt;0.<\/p>\n<p><strong>How Are Exponential Functions Graphed?<\/strong><br \/>\nWhen exponential functions are graphed in the coordinate plane, they follow a smooth curve with some special properties.\u00a0 Very small changes in the exponent x cause the graph to become more and more steep.\u00a0 In addition, as the exponent x becomes smaller, the curve will get smaller and closer to the x axis, but it never touches it, no matter how small x becomes.<\/p>\n<p><strong>What Is the Logarithmic Function?<\/strong><br \/>\nThe logarithmic function is the inverse of the exponential function.\u00a0 If x =a<sup>y<\/sup>, then y = log<sub>a<\/sub>x.\u00a0 For example, 2<sup>3 = <\/sup>8, and log<sub>2<\/sub>8 = 3, whenever a is not equal to 1 and &gt;0.\u00a0 Common logarithmic functions are logarithms of 10, which are often just written without\u00a0 the 10 in the subscript.\u00a0 They mean the same thing, though, so that log<sub>10<\/sub>x means the same thing as log x.<\/p>\n<p><strong>Why Are Exponential Functions Important?<\/strong><br \/>\nExponential functions are useful in many common applications, such as compounding interest. Population growth also follows an exponential function,\u00a0 as do many relationships in biology and economics.\u00a0 Radioactive decay also follows an exponential relationship.<\/p>\n<p><strong>Why Are Logarithmic Functions Important?<\/strong><br \/>\nLogarithmic functions are a type of shorthand underlying important mathematical relationships. Many different scales, such as decibels measuring sound, are logarithmic.\u00a0 The pH measurement of acidity is also a logarithmic scale.\u00a0 They also have many useful applications in the measurement of musical intervals and perception.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/math-tutoring\/\">math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Richmond, VA visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-richmond-virginia\/\">Tutoring in Richmond, VA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview:\u00a0 What Are Exponential Functions? Exponential functions are a special type of mathematical functions that follow the formula y = ax.\u00a0 The constant a and the exponent x are both real numbers.\u00a0 In addition, a is not equal to 1 and a &gt;0. How Are Exponential Functions Graphed? When exponential functions are graphed in the [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[633],"class_list":["post-5653","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-exponential-functions-logarithmic-functions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5653","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=5653"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5653\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5653"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5653"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}