solving an exponential as a variable

**Tren301** · July 4th 2012, 10:02 PM

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.

**Prove It** · July 4th 2012, 10:28 PM

Originally Posted by Tren301

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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