# What is the equation below solved for x to the nearest hundredth?

## ${\log}_{5} \left(x + 2\right) + {\log}_{5} 7 = 1$

Oct 3, 2016

$x = - \frac{9}{7}$

#### Explanation:

This is what I did to solve it:

You can multiply the $x + 2$ and the $7$ and it will turn into:

${\log}_{5} \left(7 x + 14\right)$

Then the $1$ can be turned into:

${\log}_{\text{5}} 5$

The current state of the equation is:

${\log}_{5} \left(7 x + 14\right) = {\log}_{\text{5}} 5$

You can then cancel the "logs" out and it will leave you with:

$\textcolor{red}{\cancel{{\textcolor{b l a c k}{\log}}_{\textcolor{b l a c k}{5}}}} \left(7 x + 14\right) = \textcolor{red}{\cancel{{\textcolor{b l a c k}{\log}}_{\textcolor{b l a c k}{\text{5}}}}} 5$

$7 x + 14 = 5$

From here you just solve for x:

$7 x \textcolor{red}{\cancel{\textcolor{b l a c k}{- 14}}} = 5 - 14$

$7 x = - 9$

$\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x = - \frac{9}{7}$

If somebody could double check my answer that would be great!