Question

How do you solve `log x=-2`?

Answer 1

`x=1/100`.

Explanation:

You only need to know that the logarithm is the inverse function of the exponential.

If by "`log`" you mean the base 10 logarithm, then simply make both terms the exponents of a `10`-based power:

`log(x)=-2 \implies 10^{log(x)}=10^{-2}`

Now, as I said, exponential and log are inverse function, which means that they cancel out, remaining with

`x=10^{-2}=1/100`

If you have another base, simply substitute that, replacing 10 with your base.