Question

If $x , y , z$ are in G.P. and $a ^ { x } = b ^ { y } = c ^ { z }$, then.

• A. $\log _ { a } c = \log _ { b } a$
• B. $\log _ { b } a = \log _ { c } b$
• C. $\log _ { c } b = \log _ { a } c$
• D. None of these

Answer 1

Answer: (B)

$\log _ { b } a = \log _ { c } b$

Answer 2

$x , y , z$are in G.P., then

Now $a ^ { x } = b ^ { y } = c ^ { z } = m$

$\Rightarrow$ $x \log _ { e } a = y \log _ { e } b = z \log _ { e } c = \log _ { e } m$

$\Rightarrow$ $x = \log _ { a } m , y = \log _ { b } m , z = \log _ { c } m$

Again as $x , y , z$ are in G.P., so $\frac { y } { x } = \frac { z } { y }$

$\Rightarrow$ $\frac { \log _ { b } m } { \log _ { a } m } = \frac { \log _ { c } m } { \log _ { b } m }$ $\Rightarrow$ $\log _ { b } a = \log _ { c } b$.