Question

Evaluate the following:

4 log 2 + 3 log 5 – log 2

Answer 1

4 log 2 + 3 log 5 – log 2

Using the rule n log ⁡a = log ⁡aⁿ,

log 2⁴ + log 5³ – log 2

Simplify the powers:

2⁴ = 16, 5³ = 125

∴ log 16 + log 125 – log 2

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

= `log ((16 xx 125)/2)`

= `log (2000/2)`

= log 1000

= 3