Question

If $a=b^{2x}$, $b=c^{2y}$, $c=a^{2z}$, then $xyz=$

• A. $2^{-2}$
• B. $2^{-3}$
• C. $2^2$
• D. $2^3$

Answer 1

Answer: (B)

$2^{-3}$

$a=b^{2x};b=c^{2y};c=a^{2z}$

$\Rightarrow \log a=\log b^{2x}=2x\log b$

$\Rightarrow 2x=\frac{\log a}{\log b}$$\Rightarrow x=\frac{1}{2}.\frac{\log a}{\log b}$

Similarly,

$y=\frac{1}{2}.\frac{\log b}{\log c}$

and,

$z=\frac{1}{2}.\frac{\log c}{\log a}$

$\therefore xyz=\frac{1}{8}=2^{-3}$