# solving an exponential as a variable

• Jul 4th 2012, 11:02 PM
Tren301
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.(Hi)
• Jul 4th 2012, 11:28 PM
Prove It
Re: solving an exponential as a variable
Quote:

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.(Hi)

\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*}.