How would I evaluate this logarithm: log (base 3) (24)

Answer 1

Set this equal to a variable: log₃24 = x

Rewrite in exponential form: 3^x = 24

This is not easy to solve, so instead we can use a trick, where we take the common log (meaning base 10) of both sides:

log 3^x = log 24

There is a rule of logarithms that allows us to drop the exponent, x, in front of the log:

x log 3 = log 24

To solve for x, divide both sides by log 3:

x = (log 24)/(log 3)

Since these are both base 10, you can enter this into your calculator:

x = 2.89278926071