# How do you solve  ln x^3 = 2 ln 5 - 3 ln 2?

Apr 21, 2016

$x = \sqrt[3]{\frac{25}{8}} = \frac{\sqrt[3]{25}}{2}$

#### Explanation:

$\ln {x}^{3} - 2 \ln 5 + 3 \ln 2 = 0$
$\ln {x}^{3} - \ln {5}^{2} + \ln {2}^{3} = 0$
$\ln {x}^{3} - \ln 25 + \ln 8 = 0$
$\ln \left(\frac{8 {x}^{3}}{25}\right) = 0$
${e}^{0} = \frac{8 {x}^{3}}{25}$

$1 = \frac{8 {x}^{3}}{25}$

$25 = 8 {x}^{3}$

$\frac{25}{8} = {x}^{3}$

$x = \sqrt[3]{\frac{25}{8}} = \frac{\sqrt[3]{25}}{2}$