Question

How do you solve `4^(x-1)=3`?

Answer 1

You can try by taking the logarithm (of base `4`) of both sides:
`log_4(4^(x-1))=log_4(3)`
`log_4` and `4^()` cancel out, so you get:
`x-1=log_4(3)` and
`x=1+log_4(3)`

This can be a little tricky to solve unless you decide to change base and can use a calculator (or tables):
`log_4(3)=(ln3)/(ln4)~~0.8` (using natural logarithms)
So that:
`x=1.8`