Question

Express as a single logarithm:

`1/2 log 36 + 2 log 5 - 3 log 2`

Answer 1

`1/2 log 36 + 2 log 5 - 3 log 2`

Using the rule n log ⁡a = log ⁡aⁿ,

= `log 36^(1/2)  +  log 5^2  -  log 2^3`

Simplify:

`36^(1/2) = 6

5² = 25

2³ = 8

∴ log 6 + log 25 – log 8

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

= `log ((6 xx 25)/8)`

= `log (150/8)`

= `log (75/4)`