Question

Express as a single logarithm:

`log 2 - 1/3 log 125 + 1/4 log 81`

Answer 1

`log 2 - 1/3 log 125 + 1/4 log 81`

Using the rule n log ⁡a = log ⁡aⁿ,

= `log 2 - log 125^(1/3)  +  log 81^(1/4)`

Now, `125^(1/3)` = 5 and `81^(1/4)` = 3

∴ log 2 – log 5 + log 3

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

= `log((2 xx 3)/5)`

= `log (6/5)`