Question

Evaluate the following:

1 + 3 log 5 + 3 log 2

Answer 1

1 + 3 log 5 + 3 log 2

We know that

1 = log 10  ....(since base is 10)

∴ log 10 + 3 log 5 + 3 log 2

Using the rule n log ⁡a = log ⁡aⁿ,

log 10 + log 5³ + log 2³

Simplify the powers:

5³ = 125

2³ = 8

∴ log 10 + log 125 + log 8

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

= log (10 × 125 × 8)

= log (10000)

= 4