# How do you condense log 40 - log 4 ?

May 11, 2018

$\log 40 - \log 4$ = $\log \left(\frac{40}{4}\right)$ = $\log 10 = 1$

#### Explanation:

Use the quotient property of logarithms,
${\log}_{b} \left(x\right) - {\log}_{b} \left(y\right)$ = ${\log}_{b} \left(\frac{x}{y}\right)$

$\log 40 - \log 4$ = $\log \left(\frac{40}{4}\right)$ = $\log 10 = 1$

Note:
${\log}_{b} \left(b\right) = 1$ ---> hence ${\log}_{10} \left(10\right) = 1$