# find $x$ from logarithm expression for $\log_{10}$ fraction

$$\log_{10} x = 0.5$$

I know if $\log_{10} x = 2$ then $x$ is $100$ but I don't know how to work out for a non obvious answer.

## 2 Answers

To find the answer, we convert from logarithmic form to exponential form.

$\log_{10} x = 0.5 \iff 10^{\frac{1}{2}}=x$.

Then just use your calculator. The general formula is $\log_b x = p \iff b^p=x.$

$$\log_bn=p\Leftrightarrow b^p=n.$$

I chose $b$ for base, $p$ for power and $n$ for number.

You need to know what $10^{0.5}=10^{1/2}$ is to answer your specific question.