Question

If A = 1 + r^a + r^2a + r^3a + ….¥ and B = 1 + r^b + r^2b + r^3b + ….¥ , then is equal to –

• A. log_B A
• B. log_1–B (1 – A)
• C. $\log _ { \frac { B - 1 } { } } ^ { B }$
• D. None of these

Answer 1

Answer: (C)

$\log _ { \frac { B - 1 } { } } ^ { B }$

Answer 2

A = ̃ 1 – r^a = $\frac { 1 } { \mathrm {~A} }$ ̃ r^a = 1 – =

B = $\frac { 1 } { 1 - r ^ { b } }$ ̃ 1 – r^b = $\frac { 1 } { B }$ ̃ r^b = 1 – = $\frac { B - 1 } { B }$

\ a log r = log $\left( \frac { \mathrm { A } - 1 } { \mathrm {~A} } \right)$ and b log r = log $\left( \frac { B - 1 } { B } \right)$

\ $\frac { \mathrm { a } } { \mathrm { b } }$ = = $\left( \frac { \mathrm { A } - 1 } { \mathrm {~A} } \right)$ .

Hence (3) is the correct answer.