# How do you solve -2log_5(7x)=2?

Jul 27, 2016

$x = \frac{1}{35}$

#### Explanation:

You can divide all terms by 2 and have:

${\log}_{5} \left(7 x\right) = - 1$

you can note that

$- 1 = {\log}_{5} \left(\frac{1}{5}\right)$

so you can substitute:

${\log}_{5} \left(7 x\right) = {\log}_{5} \left(\frac{1}{5}\right)$

that's equivalent to:

$7 x = \frac{1}{5} \mathmr{and} x > 0$

$x = \frac{1}{35}$