# How do you solve 3^x=3sqrt2?

Nov 4, 2016

$x = \ln \frac{18}{\ln} 9$

#### Explanation:

Take the natural logarithm of both sides.

$\ln \left({3}^{x}\right) = \ln \left(3 \sqrt{2}\right)$

Use the logarithm rule $\ln {a}^{n} = n \ln a$.

$x \ln 3 = \ln \left(3 \sqrt{2}\right)$

$x \ln 3 = \ln \left(\sqrt{18}\right)$

Use the same logarithm rule as above.

$x = \ln {\left(18\right)}^{\frac{1}{2}} / \ln 3$

$x = \frac{\frac{1}{2} \ln 18}{\ln} 3$

$x = \ln \frac{18}{2 \ln 3}$

$x = \ln \frac{18}{\ln} 9$

Hopefully this helps!