Question

How do you solve `log_3 32 = x`?

Answer 1

This is already 'solved' in that `x = log_3 32`

but you can use the change of base formula to find:

`x = log(32)/log(3) = ln(32)/ln(3) ~~ 3.15465`

Explanation:

The change of base formula tells use that if `a, b, c > 0` then:

`log_a b = (log_c b)/(log_c a)`

This allows us to express `log_3 32` in terms of common (base `10`) logarithms or natural (base `e`) logarithms:

`log_3 32 = log(32)/log(3) = ln(32)/ln(3) ~~ 3.15465`