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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)−21.8 –  Reader Oct 22 '12 at 9:54
    
Thanks Marc van Leeuwen for editing. –  Reader Oct 22 '12 at 10:23
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2 Answers 2

up vote 1 down vote accepted

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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Thanks Babak Sorouh –  Reader Oct 22 '12 at 10:21
    
Right to the point! +1 –  amWhy Mar 31 '13 at 0:23
    
@amWhy: Thanks Amy. You know, sometimes, my solutions here looks strange to me. Especially, when they were done before. :-) –  B. S. Mar 31 '13 at 2:18
    
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. –  amWhy Mar 31 '13 at 2:21
    
@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. :-) –  B. S. Mar 31 '13 at 3:05
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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 Peter –  Reader Oct 22 '12 at 10:22
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