Question

Simplify the following:

`log 625/log 5`

Answer 1

Step 1: We know that

`(log ⁡a)/(log ⁡b) = log_b a`

So, `log 625/log 5 = log_5 625`

Step 2: Express 625 as a power of 5:

625 = 5⁴

Step 3: log₅ 625 = log₅ (5⁴)

= 4 log₅ 5

Since log_⁡5 5 = 1,

log₅ 625 = 4