Question

Write log8 3 as a logarithm of base 5.

1) (log3)5/(log8)5
2) (log5)3/(log5)8
3) (log8)5/(log3)5
4) (log5)8/(log5)3 ...?

Answer 1

The answer is 2) (log5)3/(log5)8

We will use the change-of-base formula:
`log_a(x)= (log_b(x))/(log_b(a))`

So, if we want to write log8 3 as a logarithm of base 5, in these example a = 8, x = 3, b = 5:

`log_8(3)= (log_5(3))/(log_5(8))`