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Math Help - solving an exponential as a variable

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    solving an exponential as a variable

    Hi,
    I have a simple question; 10^x= 10000 . I know the answer is x=4, but what I want to know is how do I find the value of x algebraically. I looked on some websites, and they suggested finding the log or what but I havn't done logs yet.

    Tren301.
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    Re: solving an exponential as a variable

    Quote Originally Posted by Tren301 View Post
    Hi,
    I have a simple question; 10^x= 10000 . I know the answer is x=4, but what I want to know is how do I find the value of x algebraically. I looked on some websites, and they suggested finding the log or what but I havn't done logs yet.

    Tren301.
    \displaystyle \begin{align*} 10^x &= 10\,000 \\ \log_{10}{\left(10^x\right)} &= \log_{10}{\left(10\,000\right)} \\ x &= \log_{10}{\left(10^{4}\right)} \\ x &= 4 \end{align*}

    Technically the logarithms are redundant though, since it can be seen from inspection that \displaystyle \begin{align*} 10^4 = 10\,000 \end{align*}.
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