# How do you solve log_7(-2b+10)=log_7(3b)?

$b = 2$

#### Explanation:

The solution

${\log}_{7} \left(- 2 b + 10\right) = {\log}_{7} \left(3 b\right)$

Take the anti-logarithm of both sides of the equation

${7}^{{\log}_{7} \left(- 2 b + 10\right)} = {7}^{{\log}_{7} \left(3 b\right)}$

$- 2 b + 10 = 3 b$

Solving for b

$3 b + 2 b = 10$

$5 b = 10$

$\frac{5 b}{5} = \frac{10}{5}$

$b = 2$

God bless....I hope the explanation is useful.