Question

(i) log m – log n = log (mⁿ)

(ii) If log₁₀ (x + 5) + log₁₀ (x – 5) = log 600, then x = 5

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

(i) False - The correct law is `log m - log n = log (m/n); log (m^n)` equals n · log m, not log m – log n.

(ii) False - Combine the logs:

log₁₀ (x + 5)(x – 5) = log₁₀ 600

⇒ x² − 25 = 600 

⇒ x² = 625

So x = ±25.

But the domain requires x – 5 > 0.

So x = 25 (not 5).