Question

Evaluate the following:

`log_(6sqrt(2)) 72`

Answer 1

Given: `log_(6sqrt(2)) 72`

Step-wise calculation:

1. Let `x = log_(6sqrt(2)) 72`,

So `(6sqrt(2))^x = 72`.

2. Observe `6sqrt(2) = sqrt(72)`,

So `(6sqrt(2))^x = (sqrt(72))^x`

`(6sqrt(2))^x = (72^(1/2))^x`

`(6sqrt(2))^x = 72^(x/2)`

3. Therefore `72^(x/2) = 72^1`,

So `x/2 = 1` and x = 2.