Question

Express as a single logarithm:

`2 + 1/3 log 8 - 2 log 5`

Answer 1

`2 + 1/3 log 8 - 2 log 5`

We know that

2 = log 100  ...(Since log 10² = 2)

∴ `log 100 + 1/3log 8  - 2 log 5`

Using the rule n log a = log aⁿ, we get:

= `log 100 + log 8^(1/3) - log 5^2`

Simplify the powers:

`8^(1/3)` = 2

5² = 25

∴ log 100 + log 2 – log 25

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

= `log ((100 xx 2)/25)`

= `log (200/25)`

= log 8