# How do you solve 3lnx+ln5=7?

Nov 26, 2015

Use the properties of logs ...

#### Explanation:

$3 \ln x + \ln 5 = \ln \left[\left(5\right) \left({x}^{3}\right)\right]$

Now, exponentiate both sides of the equation ...

${e}^{\ln} \left[\left(5\right) \left({x}^{3}\right)\right] = {e}^{7}$

Simplify and solve for x...

$5 {x}^{3} = {e}^{7}$

${x}^{3} = \frac{{e}^{7}}{5}$

${\left({x}^{3}\right)}^{\frac{1}{3}} = x = {\left[\frac{{e}^{7}}{5}\right]}^{\frac{1}{3}} \approx 6.031$

hope that helped