How do you solve $4^x=3$ ?

Question

1127 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-06T17:43:00

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 $x<1$
$x = 0.792$

$4^x = 3$

$log4^x = log3$
$x log 4 =log 3$

$x = (log3)/(log4)$

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

How do you solve 4^x=3 4^x=3 ?