Natural Logarithms? Help please?

Let x = log₇(4)

This means that

7^x = 4

Take the natural log of both sides (ln means log to base e)

ln(7^x) = ln(4)

By a property of logarithms (see the Formulary at the top of this page) we have

x*ln(7) = ln(4)

so x = ln(4)/ln(7) or, substituting for x from the first line above):

log₇(4) = ln(4)/ln(7)