How do you solve log x=-2?

Jun 19, 2016

$x = \frac{1}{100}$.

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:

$\log \left(x\right) = - 2 \setminus \implies {10}^{\log \left(x\right)} = {10}^{- 2}$

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

$x = {10}^{- 2} = \frac{1}{100}$

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