Question

How do I find the natural log of a fraction?

Answer 1

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`)

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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.