Thread: Help on solving an equation

This is a question from the paper 1 of the last year's IB Math (HL) exam that my teacher gave out today.

Q: Solve the equation 4^(x-1)=2^x+8.

4^(x-1)=2^x+8
4^x*4^(-1)=2^x+8
4^(-1)=(1/2)^x+8/4^x
4^(-1)=1/2^x+8/4^x

Then I am stuck here.

I do know that the answer is 3 but I need to know the steps and working that lead to the answer in order to obtain full marks on the exam. Some help will be really appreciated!

4^x*4^(-1)=2^x+8

Represent as .