Originally Posted by

**FinnSkies** Hi,

I'm new to the forum, but decided to give it a try now, because I can't seem to get around what I'm doing wrong. I'm revising for my IB finals and can't seem to get this one question down, which is from a past final exam:

So the question is: Solve the equation $\displaystyle 4^{x-1}=2^x+8$

My method:

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

4^(x-1) = 2^x+2^3

2^(2(x-1)) = 2^x+2^3

2^(2x-2) = 2^x+2^3

log 2 (2^(2x-2)) = log 2 (2^x) + log 2 (8) Unfortunately, no. This is the mistake. $\displaystyle Log(a+b)\neq Log(a)+Log(b)$ Taking logs of both sides will lead you to a dead end here. Review this stage carefully, you've not taken logs of the right hand side correctly.