If 2 2x = 15, what is x?

Take the log of base 2 of each side.

2x = log2 15

2x = 3.90...

x = 3.9/2 = 1.9534...

If 2^(2x) = 15, what is x?

$2^{2x}=15\\ log2^{2x}=log15\qquad \mbox{This is true what ever base you use so why not use base 10 }\\ 2xlog2=log15\\ 2x=\frac{log15}{log2}\\ x=\frac{log15}{2log2}\\$

(log(15)/(2*log(2))) = 1.9534452978042593