# How do you solve 2+log_3(2x+5)-log_3x=4?

Feb 8, 2015

I would start by collecting the logs on one side:

${\log}_{3} \left(2 x + 5\right) - {\log}_{3} \left(x\right) = 4 - 2$

I can use the fact that:
$\log M + \log N = \log \left(\frac{M}{N}\right)$
Giving:

${\log}_{3} \left(\frac{2 x + 5}{x}\right) = 2$

Use the definition of logarithm:

${\log}_{a} x = b \to {a}^{b} = x$

Giving:

$\frac{2 x + 5}{x} = {3}^{2}$
$2 x + 5 = 9 x$
$7 x = 5$
$x = \frac{5}{7}$

hope it helps