Question

Evaluate the following:

`2 log 6 - 2 log 3 + 1/2 log 625`

Answer 1

`2 log 6 - 2 log 3 + 1/2 log 625`

Using the rule n log ⁡a = log ⁡aⁿ,

`log 6^2 - log 3^2 + log 625^(1/2)`

Simplify the powers:

6² = 36

3² = 9

`625^(1/2)` = 25

∴ log 36 − log 9 + log 25

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

= `log (36/9) + log 25`

= log 4 + log 25

= log (4 × 25)

= log 100

= 2