If x = _b a, , ,y = _c b, , , ,z = _a c, then xyz is - Vidyadip

MCQ

If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is

A
$0$
✓
$1$
C
$3$
D
None of these

✓

Answer

Correct option: B.

$1$

b
(b) We have $xyz = {\log _b}a \times {\log _c}b \times {\log _a}c$

$ = {{{{\log }_e}a} \over {{{\log }_e}b}} \times {{{{\log }_e}b} \over {{{\log }_e}c}} \times {{{{\log }_e}c} \over {{{\log }_e}a}} = 1$.

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