Question

Evaluate the following:

`log 8 + 2 log 5 - 1/3 log 8`

Answer 1

`log 8 + 2 log 5 - 1/3 log 8`

Using the rule n log ⁡a = log ⁡aⁿ,

`log 8 + log 5^2 - log 8^(1/3)`

Simplify the powers:

5² = 25

`8^(1/3)` = 2

log 8 + log 25 − log 2

Using the rules log ⁡a − log ⁡b = `log⁡(a/b)` and log⁡ a + log ⁡b = log ⁡(ab),

= `log ((8 xx 25)/2)`

= `log (200/2)`

= log 100

= 2