Question

How do you write the logarithmic expression as the sum, difference, or multiple of logarithms and simplify as much as possible for `log_5(25/x)`?

Answer 1

`log_5(25/x) = 2 - log_5x`

Explanation:

Property: `log_b(x/y) = log_b x – log_b y`

So

`log_5(25/x) = log_5(25) – log_5x`

`log_5(25/x) = log_5(5^2) – log_5x`

Property: `log_b(x^d) =dlog_b x`

So

`log_5(25/x) = log_5(5^2) – log_5x = 2log_5(5) – log_5x`

`log_5(25/x) = = (2×1) – log_5x`

`log_5(25/x) = = 2 – log_5x`