# How do you solve 4^x=3 ?

May 6, 2016

The first thing we should realise is that 3 is not a power of 4, so this will have to be solved by logs. ${4}^{1} = 4$ , so $x < 1$
$x = 0.792$

#### Explanation:

${4}^{x} = 3$

$\log {4}^{x} = \log 3$
$x \log 4 = \log 3$

$x = \frac{\log 3}{\log 4}$

There are no log laws to simplify this, it has to be done on a calculator: $x = 0.792$