Answer
$x = -2$
Work Step by Step
Rewrite $100$ as an exponential expression:
$10^{x} = \frac{1}{10^{2}}$
Since the exponent is in the denominator, rewrite the exponential expression using a negative exponent to get rid of the fraction (use the rule $\frac{1}{a^m}=a^{-m}$:
$10^{x} = 10^{-2}$
If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $x$:
$x = -2$
