Comparing exponentials with logarithms

Project Euler problem 99 is as follows:

Comparing two numbers written in index form like 211 and 37 is not difficult, as any calculator would confirm that 211 = 2048 < 37 = 2187.

However, confirming that 632382518061 < 519432525806 would be much more difficult, as both numbers contain over three million digits.

Using base_exp.txt, a 22K text file containing one thousand lines with a base/exponent pair on each line, determine which line number has the greatest numerical value.

This had me stumped for a while because, as far as I could find, there is simply no realistic way of calculating the large exponentials in the list. And then I learned something:

log(xy) = ylog(x)

And once you know that, finding the solution is very easy indeed.

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