# Given log4=0.6021, log9=0.9542, and log12=1.-792, how do you find log 400,000?

Jan 21, 2017

$\log 400 , 000 = 5.6021$

#### Explanation:

$\log 400 , 000$

= $\log \left(4 \times 100 , 000\right)$

= $\log \left(4 \times {10}^{5}\right)$

As $\log \left(m \times n\right) = \log m + \log n$ and $\log {a}^{n} = n \log a$,

we can write te above as

$\log 4 + 5 \log 10$

but $\log 10 = 1$

Hence $\log 400 , 000 = \log 4 + 5 \times 1 = 0.6021 + 5 = 5.6021$

Note : Value of $\log 9$ and $\log 12$ is not needed.