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If a function of this form $f(x)=b\cdot a^x$ is called an exponential function, then is the function $g(d)=13.4\cdot \ln(d)-21.8$ also exponential?

If yes why?

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    g(d)=13.4⋅ln(d)−21.82012-10-22
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    Thanks Marc van Leeuwen for editing.2012-10-22

2 Answers 2

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It is $f(x)=a^{\log_a (b)+x}$ provided $a\ne0, a>0$ which is clearly not an exponential function.

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    Right to the point! +12013-03-31
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    @amWhy: Thanks Amy. You know, sometimes, my solutions here looks strange to me. Especially, when they were done before. :-)2013-03-31
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    I understand. Sometimes I look at older posts of mine (from 2011) and cringe. But no need for you to cringe at this solution ;-) I reached "2 years" as a member at Math.SE. I started out just watching...then jumped in, but then took a long time off, away from the site, nearly a year, before actively participating again.2013-03-31
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    @amWhy: Dear Amy; I forgot to thank you for supporting me in that question with TB. And forgive me if I made you to do that while you didn't want to. I wanted to tell you these before you get your bed. Wish you a dreamy sleep in Heaven my dear friend. :-)2013-03-31
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    Don't mention it. I didn't feel at all like you "made me" do it. I very much wanted to, because I care very much about you, and about OPs and users in general, and sometimes users forget that we are all: both askers, and answerers, human beings with feelings that matter! ;-)2013-03-31
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No, it's a transformation of the natural log function, which is the inverse of the exponential.

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    Thanks for the answer Peter2012-10-22