# How do you solve 4^x= 7?

##### 1 Answer
Jul 17, 2015

I found: $x = 1.4036$

#### Explanation:

If you can use a pocket calculator (or tables) you could change it into a log using the definition of logarithm:
${\log}_{a} b = x \to {a}^{x} = b$
where in your case you get:
${\log}_{4} \left(7\right) = x$
you can now change base of your log to evaluate it using a pocket calculator (for example, using the base $e$ of the natural logarithm, $\ln$):
$x = {\log}_{4} \left(7\right) = \frac{\ln \left(7\right)}{\ln \left(4\right)} = 1.4036$