# How do you solve log x + log 4 = 2?

Jan 25, 2016

The answer is $x = 25$

#### Explanation:

$\log x + \log 4 = 2$

First we use the identity which says that: $\log a + \log b = \log \left(a \cdot b\right)$

$\log \left(4 x\right) = 2$

Then we change the number on the right side to a logarythm using a formula:

$a = {\log}_{b} \left({b}^{a}\right)$

$\log \left(4 x\right) = \log 100$

Now we can skip the logarythm signs because both sides are single logarythms with the same base.

$4 x = 100$

$x = 25$