# How do you solve 3 + 2 ln x = 10?

##### 1 Answer
Aug 12, 2015

$\textcolor{red}{x = {e}^{\frac{7}{2}}}$

#### Explanation:

$3 + 2 \ln x = 10$

Subtract $3$ from each side.

$2 \ln x = 7$

Divide each side by $2$.

$\ln x = \frac{7}{2}$

Convert the logarithmic equation to an exponential equation.

${e}^{\ln} x = {e}^{\frac{7}{2}}$

Remember that ${e}^{\ln} x = x$, so

$x = {e}^{\frac{7}{2}}$

Check:

$3 + 2 \ln x = 10$

If $x = {e}^{\frac{7}{2}}$,

$3 + 2 \ln {e}^{\frac{7}{2}} = 10$

$3 + 2 \left(\frac{7}{2}\right) = 10$

$3 + 7 = 10$

$10 = 10$

$x = {e}^{\frac{7}{2}}$ is a solution.