Question

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

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

1

Answer 2

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

⇒ $x = \frac{\log b}{\log a} = \log_{a}b$

Similarly $y = \log_{b}c,z = \log_{c}a$

$x\ln a = y\ln b = xy\ln(ab) = k(\text{say})xyz = \log_{a}b.\log_{b}c.\log_{c}a = 1$.