# How do you solve log_10(x+7) - log_10(x-7)=1?

##### 1 Answer
Nov 12, 2015

Part solution given. It has been taken to a point that is much easier to solve.

#### Explanation:

You are dealing with logs in that the $\textcolor{b l u e}{\text{all}}$ of the left is logs. Consequently the value on the right is a value obtained from taking a log

Let b be a constant
Write the right hand side as :
$\to {\log}_{10} \left(b\right) = 1$

${10}^{1} = b \text{ so } b = 10$

Subtraction of logs is the consequence of division of the source values. So now we have:

$\frac{x + 7}{x - 7} = 10$

$\implies x + 7 = 10 x - 70$

I will let you take over from this point and complete the calculations.