Let's say I knew that 64 was a power of 2 and I wanted to know what power of two it was but I didn't want to multiply two by it's self those y amount of times to find out. How would I go about doing this? Or to make it so it has a more practical application let x equal 13 and z equal 347647 I have no idea if z is in fact a power of 13 I don't even know if it's divisible by 13 but it shouldn't matter right, you would just get a number and a decimal as your value of y.
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ln(x^y) = ln(z)
y*ln(x) = ln(z)
y = ln(z) / ln(x)
y*ln(x) = ln(z)
y = ln(z) / ln(x)