# How do you solve the equation log_7 24-log_7(y+5)=log_7 8?

Dec 2, 2016

$y = - 2$

#### Explanation:

${\log}_{7} 24 - {\log}_{7} \left(y + 5\right) = {\log}_{7} 8$

$\Leftrightarrow {\log}_{7} \left(\frac{24}{y + 5}\right) = {\log}_{7} 8$

hence $\frac{24}{y + 5} = 8$

or $24 = 8 \times \left(y + 5\right)$

or $y + 5 = \frac{24}{8} = 3$

and $y = 3 - 5 = - 2$