Question

If $a^x=b,b^y=c,c^z=a$, then the value of xyz is

• A. 0
• B. 1
• C. $\frac{1}{abc}$
• D. abc

Answer 1

The correct option is B 1

We have,

$a^x=b,b^y=c,c^z=a$

On taking $\log$ both side, we get

$x\log a=\log b$

$x=\frac{\log b}{\log a}$ …… (1)

Similarly,

$y=\frac{\log c}{\log b}$ …….. (2)

$z=\frac{\log a}{\log c}$ ……. (3)

From equation (1), (2) and (3) , we get

$xyz=\frac{\log b}{\log a}\times \frac{\log c}{\log b}\times \frac{\log a}{\log c}$

$xyz=1$

Hence, this is the answer.