Question

Express as a single logarithm:

3 – 2 log 5 + 3 log 2

Answer 1

3 – 2 log 5 + 3 log 2

We know that

3 = log 1000  ...(Since log 10³ = 3)

∴ log 1000 − 2 log 5 + 3 log 2

Using the rule n log ⁡a = log ⁡aⁿ,

log 1000 − log 5² + log 2³

Simplify the powers:

5² = 25, 2³ = 8

∴ log 1000 – log 25 + log 8

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

= `log ((1000 xx 8)/25)`

= `log (8000/25)`

= log 320