Question

If log_e$\left( \frac{a + b}{2} \right)$ = $\frac{1}{2}$ (log_ea + log_eb) then relation between a & b is –

• A. a = b
• B. a = 2b
• C. a = $\frac{b}{2}$
• D. None

Answer 1

Answer: (A)

a = b

Answer 2

log_e $\left( \frac{a + b}{2} \right)$ = $\frac{1}{2}$ log (ab)

$\frac{a + b}{2}$ = $\sqrt{ab}$

a + b – $2\sqrt{ab}$ = 0

($\sqrt{a}$ – $\sqrt{b}$)² = 0 Ž $\sqrt{a}$ = $\sqrt{b}$ Ž a = b