# Question #c9ece

Jun 7, 2017

$x = - 2$

#### Explanation:

First, let's recall what it means when an ordered pair is lying on the graph of an equation. When an ordered pair is said to be lying on the graph of an equation, it means that the ordered pair's $x$ and $y$ values satisfy the equation.

Now, armed with this knowledge, we can start working on the problem. Here, we are trying to find an $x$ value such that it and the $y$ value in the ordered pair $\left(x , \frac{1}{100}\right)$ will satisfy the equation $y = {10}^{x}$.

Since we already know the $y$ value, we can substitute it into the equation. And then we can solve for $x$.

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

Now we just need to find out what $x$ is. We notice that $\frac{1}{100}$ can be rewritten as $\frac{1}{10} ^ 2$. And we also recall the definition of negative exponents: ${a}^{- b} = \left(\frac{1}{a} ^ b\right)$. Combining the definition of negative exponents and the rewritten form of $\frac{1}{100}$, we can find $x$:

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

As you can see, $x = - 2$.