# How do you use the properties of logarithms to rewrite and simplify the logarithmic expression of log (7/100)?

Jun 22, 2015

First use the division-to-subtraction rule

#### Explanation:

$\log \left(\frac{7}{100}\right) = \log 7 - \log 100$
Then remember that $100 = {10}^{2}$
And that you may always put the exponent before the log:
$= \log 7 - \log {10}^{2} = \log 7 - 2 \cdot \log 10$

And since $\log 10 = {\log}_{10} 10 = 1$:
$= \log 7 - 2$