# How do you solve 125^(2x+1)/625^(x+2)=3125^(x+2)?

Sep 19, 2016

$x = - 5$

#### Explanation:

$\frac{{125}^{2 x + 1}}{{625}^{x + 2}} = {3125}^{x + 2}$

or $\frac{{\left({5}^{3}\right)}^{2 x + 1}}{{\left({5}^{4}\right)}^{x + 2}} = {\left({5}^{5}\right)}^{x + 2}$

or (5^(3xx(2x+1)))/(5^(4xx(x+2)))=5^(5xx(x+2)^

or $\frac{{5}^{6 x + 3}}{{5}^{4 x + 8}} = {5}^{5 x + 10}$

or ${5}^{6 x + 3 - 4 x - 8} = {5}^{5 x + 10}$

or ${5}^{2 x - 5} = {5}^{5 x + 10}$

or $2 x - 5 = 5 x + 10$

or $2 x - 5 x = 10 + 5$

or $- 3 x = 15$

or $x = \frac{15}{-} 3 = - 5$