Question

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

• A. $\log_y \, x = \log_z \, y$
• B. $\log_x \, y = \log_z \, y$
• C. $\log_z \, b = \log_c \,b$
• D. $\log_b \, a = \log_c \, b$

Answer 1

Answer: (A)

$\log_y \, x = \log_z \, y$

Answer 2

Taking $\log$ in $x^a = y^b = z^c$
$a \, \log \: x = b \, \log \,y = c \, \log \, z$
$\frac{ \log \, x}{\log \,y} = \frac{b}{a} , \frac{\log \,y}{\log \, z} = \frac{c}{b}$
$\because \:\: a,b,c$ are in G.P,. $\:\:\: \therefore \frac{b}{a} = \frac{c}{b}$
$\therefore \frac{ \log \, x}{\log \,y} = \frac{\log \,y}{\log \, z } \Rightarrow \: \log_y x = \log_z y$