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)

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,. $\therefore \frac{b}{a}=\frac{c}{b}$
$\therefore \frac{\log x}{\log y}=\frac{\log y}{\log z}\Rightarrow {\log }_{y}x={\log }_{z}y$