NIELIT 2019 Feb Scientist C - Section C: 19

Question

If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals:

• A. $abc$
• B. $\dfrac{1}{abc}$
• C. $1$
• D. None

Answer 1

Given that:

$a^x=b ….(1)$

$b^y=c ….(2)$

$c^z=a….(3)$

taking log in above equations we get:

$\implies xlog_2 a=log_2b$

$\implies$ $x=\frac{log_2 b}{log_2 a}….(4)$

in the same way

 $y=\frac{log_2 c}{log_2 b}….(5)$

$z=\frac{log_2 a}{log_2 c}…..(6)$

multiply equations (4),(5),(6).

$\implies x*y*z=\frac{log_2b}{log_2a}*\frac{log_2c}{log_2b}*\frac{log_2a}{log_2c}$

$\implies x*y*z=1$
Option (C) is correct.

Answer 2

ANSWER: C

Take log of both side and solve.