Question

How do you approximate `log_5 (2/3)` given `log_5 2=0.4307` and `log_5 3=0.6826`?

Answer 1

`log_5(2/3) ~= -0.2519`

Explanation:

We can write `log_5(2/3)` as `log_5(2) - log_5(3)` using the rule quotient rule of logarithms that `log_a(m/n) = log_a(m) - log_a(n)`.

`log_5(2/3) = log_5(2) - log_5(3) = 0.4307 - 0.6826 = -0.2519`

Hopefully this helps!