Part of the problem is the way you have written these. Do you mean \(\displaystyle log(4^{x+2})\) or do you mean \(\displaystyle (log(4))^{x+2}\) or even \(\displaystyle \log_4{x+2}\)?
And is "logarithm" the "common logarithm", base 10, or the "natural logarithm", base e.