Question

Simplify the following:

`log 216/log 6`

Answer 1

Step 1: We know that

`(log ⁡a)/(log ⁡b) = log_b a`

So, `log 216/log 6 = log_6 216`

Step 2: Express 216 as a power of 6:

216 = 6³

Step 3: log₆ 216 = log₆ (6³)

= 3 log₆ 6

Since log_⁡6 6 = 1,

log₆ 216 = 3