{"id":24,"date":"2004-04-26T16:53:02","date_gmt":"2004-04-26T16:53:02","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=24"},"modified":"2004-04-26T16:53:02","modified_gmt":"2004-04-26T16:53:02","slug":"problem","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=24","title":{"rendered":"Problem"},"content":{"rendered":"<p>Firstly, show that: <\/p>\n<ul><img src='\/maths\/latexrender\/pictures\/135969356e1a3eecd5abfcd507de6270.gif' title='\\log_{a^n}b^n=\\log_{a}b' alt='\\log_{a^n}b^n=\\log_{a}b' align=absmiddle><\/ul>\n<p> Secondly, are there any other operations you can do to <img src='\/maths\/latexrender\/pictures\/0cc175b9c0f1b6a831c399e269772661.gif' title='a' alt='a' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/92eb5ffee6ae2fec3ad71c777531578f.gif' title='b' alt='b' align=absmiddle> and the <img src='\/maths\/latexrender\/pictures\/cb139ffd45872a9a5f17ece5cdb1d314.gif' title='\\log' alt='\\log' align=absmiddle> retains the same value? In other words:<\/p>\n<ul><i>Find all functions<\/i> <img src='\/maths\/latexrender\/pictures\/bc578f1a87b5b851e54b57e46afa2937.gif' title='f,g:\\mathbb{R^+}\\mapsto \\mathbb{R^+}' alt='f,g:\\mathbb{R^+}\\mapsto \\mathbb{R^+}' align=absmiddle> <i>such that<\/i> <img src='\/maths\/latexrender\/pictures\/66b9d280b9c102b7c6c7a6cf5599cd52.gif' title='\\log_{f(a)}g(b)=\\log_a b' alt='\\log_{f(a)}g(b)=\\log_a b' align=absmiddle> <i>for all<\/i> <img src='\/maths\/latexrender\/pictures\/028d37c9d23edbbeede0b1eb6408a742.gif' title='a,b\\in\\mathbb{R^+}' alt='a,b\\in\\mathbb{R^+}' align=absmiddle><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Firstly, show that: Secondly, are there any other operations you can do to and and the retains the same value? In other words: Find all functions such that for all<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-24","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/24","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/24\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}