{"id":13964,"date":"2016-01-19T21:05:29","date_gmt":"2016-01-19T21:05:29","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=13964"},"modified":"2018-02-13T16:01:48","modified_gmt":"2018-02-13T16:01:48","slug":"exponential-equations-converting-to-base-e-form","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/exponential-equations-converting-to-base-e-form\/","title":{"rendered":"Exponential equations:  converting to base e form"},"content":{"rendered":"<h1>The tutor points out how to convert an exponential function m<sup>x<\/sup> to e<sup>kx<\/sup>.<\/h1>\n<p>Often, when thinking of an exponential function, one might imagine the form<\/p>\n<p>y=e^(kx)<\/p>\n<p>However,<\/p>\n<p>y=m^x<\/p>\n<p>is also exponential, since the independent variable is the exponent.<\/p>\n<p>How do we convert from y=m^x to y=e^(kx)?<\/p>\n<p>First, we realize that e^(lnm)=m, since ln and e are inverses.  Next, we recall that (a^b)^c=a^(bc).<\/p>\n<p>Therefore,<\/p>\n<p>m^x=(e^(lnm))^x=e^(xlnm)<\/p>\n<p>So y=m^x can be written as y=e^(xlnm).<\/p>\n<p>HTH:)<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor points out how to convert an exponential function mx to ekx. Often, when thinking of an exponential function, one might imagine the form y=e^(kx) However, y=m^x is also exponential, since the independent variable is the exponent. How do &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/exponential-equations-converting-to-base-e-form\/\"> <span class=\"screen-reader-text\">Exponential equations:  converting to base e form<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1350,1349],"class_list":["post-13964","post","type-post","status-publish","format-standard","hentry","category-math","tag-changing-form-of-exponential-function","tag-exponential-functions"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13964","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=13964"}],"version-history":[{"count":17,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13964\/revisions"}],"predecessor-version":[{"id":29602,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13964\/revisions\/29602"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=13964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=13964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=13964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}