# How do you simplify log 100^x?

Jul 11, 2016

Recall the log rule that states $\log {a}^{n} = n \log a$:

$\log {100}^{x} = x \log 100 = x \left(\log 100\right)$

Now, remember the change of base rule ${\log}_{a} \left(n\right) = \log \frac{n}{\log} \left(a\right)$. In this case, $a = 10$.

$= x \left(\log \frac{100}{\log} 10\right)$

$= x \left(\log {10}^{2} / \log {10}^{1}\right)$

$= x \left(\frac{2 \log 10}{1 \log 10}\right)$

$= x \left(2\right)$

$= 2 x$

Hopefully this helps!