The improtant thing is the following:
ln(x * y) = ln(x) + ln(y), where x and y are positive, real numbers.

As homebody said, here you have ln(52^x) = ln(5) + xln(2). So, the solution for x is (ln(5) + ln(10))/(4*ln(10) - ln(2)) or, using our rule you can also write it as ln(50) / ln(5000), which is probably more beautiful.

Oh, I just noticed that I used the ln symbol - don’t worry about that, though, it does not matter here.