How do I find the natural log of a fraction?

1 Answer
Dec 13, 2015

Answer:

Apply the identity

#ln(a/b) = ln(a) - ln(b)#

Explanation:

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: #ln(a) = x <=> a = e^x#)


Applying these to a fraction, we get

#ln(a/b) = ln(ab^(-1)) = ln(a) + ln(b^-1) = ln(a) - ln(b)#

Thus if you can evaluate the logarithm of the numerator and of the denominator, you can evaluate the logarithm of the fraction.