How do I find the natural log of a fraction?
Apply the identity
Logarithms have the following useful properties:
#ln(ab) = ln(a) + ln(b)#
#ln(a^x) = xln(a)#
(As an exercise, try confirming these using the definition of a logarithm:
Applying these to a fraction, we get
Thus if you can evaluate the logarithm of the numerator and of the denominator, you can evaluate the logarithm of the fraction.