Question

Express as a single logarithm:

`2 log 3 - 1/2 log 4 + 1/3 log 64`

Answer 1

`2 log 3 - 1/2 log 4 + 1/3 log 64`

Using the rule n log ⁡a = log ⁡aⁿ,

= `log 3^2  -  log 4^(1/2)  +  log 64^(1/3)`

Simplify each term:

3² = 9

`4^(1/2)` = 2

`64^(1/3)` = 4

∴ log 9 – log 2 + log 4

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

= `log ((9xx4)/2)`

= `log (36/2)`

= log 18