Start by taking the natural log of both sides of the equation.
Let ln = natural log
2^(2x) = k
ln[2^(2x)] = ln(k)
When we take the natural log of both sides, exponents come down infront of the ln symbol.
So, 2x comes down and it now looks like this:
2xln(2) = ln(k)
At this point, solve the equation for x, dividing both sides by 2(ln2).
x = ln(k)/2(ln2)