# Question #b1a93

Aug 11, 2016

$x = 56$

#### Explanation:

$\log \left(x + 4\right) - \log 6 = 1$

First step. The terms must be all logs or all numbers.
Do something with the 1. We know $1 = \log 10$
(As no bases are shown, we assume they are 10.)

$\log \left(x + 4\right) - \log 6 = \log 10$

Second step
Write two log terms as one log term. single number/fraction)

If log terms are being added, then the numbers are being multiplied.
If log terms are being subtracted, then the numbers are being divided

$\log \left(\frac{x + 4}{6}\right) = \log 10$

Drop the logs on each side If log A = log B, then A = B

$\frac{x + 4}{6} = 10$

Solve the equation

$x + 4 = 60$
$x = 56$

Substitute the answer into the original equation to check .

$\log 56 - \log 6 = 1$