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 4^(x-1)=2^x+8
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
log 2 (2^(2x-2)) = log 2 (2^x) + log 2 (8)
2x-2(log 2 (2)) = x (log 2 (2)) + 3
2x-2 = x + 3
2x-x = 3 + 2
x = 5
But this doesn't check out with the original equation, because it comes to 256 = 40
It's been a while since we did logarithms and exponents, so I might be doing something incorrect. So please correct me where I'm wrong.
Thanks in advance.