Question

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

Answer 1

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`

`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`