The question is 2x log(base4)x
I believe this is product rule so I did this:
2/(ln4) + 2log(base4)x
or 2/(ln4) + log(base4)x^2
The answers give (1+lnx)1/ln2
Did I make a mistake or is that a simplification or..?
Your answer 2/(ln4) + 2log(base4)x is correct.
it may be useful to write it like this $\displaystyle \frac{2}{\ln{4}}+ \frac{2 \ln{x}}{\ln{4}}$
then use the power law$\displaystyle \ln4 = 2 \ln 2$
so giving $\displaystyle \frac{1}{\ln 2}+ \frac{ \ln x}{ \ln 2}$
$\displaystyle \Rightarrow \frac{1+\ln x}{\ln 2}$