# How do you solve 2^x=3.7?

Oct 20, 2015

$x = \log \frac{3.7}{\log 2}$ or $x \approx 1.89$

#### Explanation:

take the $\log$ of both sides:

$\log {2}^{x} = \log 3.7$

There is a rule that states that $\log {a}^{b}$ can be written as $b \cdot \log a$

$x \log 2 = \log 3.7$

$x = \log \frac{3.7}{\log 2}$ (you can use your calculator to solve this)

$x \approx 1.89$

Note:
You can also use $\ln$ instead of $\log$; your answer should be the same either way