Hi Dave,

You took the log of both sides to get

log(4^x) = log(2^x + 12)

but log(2^x + 12) is not equal to log(2^x) + log(12). What is true is that log(2^x × 12) = log(2^x) + log(12) but that's no help here.

I think your first solution is best "It's obvious the answer is 2" but another method is to use the fact that 4 = 2² and use the laws of exponents to see that 4^x = (2²)^x = 2^2x = (2^x)². Thus

4^x = 2^x + 12
(2^x)² = 2^x + 12
(2^x)² - 2^x - 12 = 0

Can you complete the solutiion?

If you need more help write back,
Harley