Question

Evaluate the following:

`log  3/4 + log  4/5 + log  5/6 - log  1/2`

Answer 1

`log  3/4 + log  4/5 + log  5/6 - log  1/2`

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

Combine all terms:

= `log (3/4 xx 4/5 xx 5/6 ÷ 1/2)`

Simplify step-by-step:

= `log ((3 xx 4 xx 5 xx 2)/(4 xx 5 xx 6 xx 1))`

Cancel common factors 4 and 5:

= `log ((3 xx 2)/6)`

= `log (6/6)`

= log (1)

= 0