Question

If `log_3 5 = x`, what is `x`?

Answer 1

`x = log_3 (5) = log(5)/log(3) ~~ 1.465`

Explanation:

`x` is the Real solution to `3^x = 5`

We can use the change of base formula:

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

with `a=3`, `b=5` and `c = 10` or `c = e` to allow the calculation of an approximation for `log_3 5` in terms of common or natural logarithms.

Using common (base `10`) logarithms:

`log_3 5 = (log_10 5) / (log_10 3) ~~ 0.69897 / 0.47712 ~~ 1.465`