I don't know if my answer is good enough for you.

As I learned from limit taking techniques of calculus, when there are power look like things in the equation, take log on both sides won't change the equality of the equation.

For the second equation of your question, take natural log on both sides, get:

ln(2^10^6)=ln(x*10^y)

ln(10^6)/ln(2)=ln(x)+ln(10^y)

ln(10^6)/ln(2)=ln(x)+y*ln(10)

now you have a y times something