Question

(i) log (m · n) = log m + log n

(ii) 3 – 5 log₁₀ 2 = log₁₀ 125 – log₁₀ 4

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i) True - Product rule for logarithms:

log_a (mn) = log_a m + log_a n for m, n > 0, a > 0, a ≠ 1.

(ii) True - Write 3 = log₁₀ (1000) 

And 5 log₁₀ 2

= log₁₀ (2⁵) 

So 3 – 5 log₁₀ 2

= log₁₀ (1000) – log₁₀ (32) 

= `log_10 (1000/32)` 

= `log_10 (125/4)` 

And `log_10 125 - log_10 4`

= `log10 (125/4)` 

So both sides are equal.