Hi guys, I'm stuck

can someone please help me understand this:

f(x) = e^(2x) log(x^2)

we are given the answer which should be : f(x)' = ( e^(2x) / ln(10) ) * (ln(x^2) + 1)

this is where I'm stuck (I'm not even sure this is right), after the product rule:

f(x)' = 2e^(2x) * ( ln(x^2)) / ln(10) ) + ( (e^(2x) * 2x) / (x^2 ln(10)) )

I am on the right track here? Thanks