After simplifying all the multiplications and divisions, you get:
Numerator: (20) * log(5) * log(e) * log(2) * log(100)
Denominator: log(20) * log(25) * log (16)
The change of base formula says that ln(20) = log(20) / log(e)
so log(e) / log(20) = 1 / ln(20)
Now, the numerator that we have left is: 20 * log(5) * log(2) * log(100)
the denominator is: ln(20) * log(25) * log(16)
Now, log(100) = 2 and log(25) = log(5^2) = 2log(5) and log(16) = log(2^4) = 4log(2)
Making these substitutions, we have:
Numerator: 20 * log(5) * log(2) * 2
Denominator: ln(20) * 2 * log(5) * 4 * log(2)
Cancelling, we end with: 5/ln(20)