Question

Simplify the following:

`log 8/log 4`

Answer 1

Step 1: We know that

`(log ⁡a)/(log ⁡b) = log_b a`

So, `log 8/log 4 = log_4 8`

Step 2: Express 8 as a power of 4:

8 = `4^(3/2)`

Step 3: log₄ 8 = `log_4 (4^(3/2))`

= `3/2 log_4 4`

Since log_⁡4 4 = 1,

log₄ 8 = `3/2`