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Math Help - L'Hopital lim (x->0) (a^x-1)/x

  1. #1
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    L'Hopital lim (x->0) (a^x-1)/x

    Good morning,

    I am doing a quick review and going over some of my completed problems here. I have the following:

     <br />
\displaystyle{\frac{\lim}{x\rightarrow0}\frac{a^x-1}{x}}<br />

    Applying L'H I got

     <br />
\displaystyle{\frac{\lim}{x\rightarrow0}\frac{\ln(  a)a^x}{1}}<br />

    Here's the problem, I don't remember why I went from a^xto ln(a)a^x.

    It's something simple, right?
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  2. #2
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    a^x = e^{\ln(a^x)}=e^{\ln(a)x}
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  3. #3
    MHF Contributor matheagle's Avatar
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    you differentiated a^x which is a^x\ln a

    just like {d\over dx}e^x=e^x\ln e=e^x
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