Question

Evaluate the following:

`1/2 log 25 + log 4 - 1/3 log 8`

Answer 1

`1/2 log 25 + log 4 - 1/3 log 8`

Using the rule n log ⁡a = log ⁡aⁿ,

`log 25^(1/2) + log 4 - log 8^(1/3)`

Simplify the powers:

`25^(1/2)` = 5

`8^(1/3)` = 2

∴ log 5 + log 4 – log 2

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

= `log ((5 xx 4)/2)`

= `log (20/2)`

= log 10

= 1