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Fundamental laws of logarithms

If xa=y, yb=z...

Question

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

A

xyz

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B

2

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C

1

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D

0.0

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Solution

The correct option is C 1
$a b c = l o g_{x} y . l o g_{y} . l o g_{z} x = l o g_{x} x = 1$
Alt. $x = z^{c} = (y^{b})^{c} = y^{b c} = (x^{a})^{b c} = x^{a b c}$
$∴ a b c = 1 \Rightarrow (c)$ .

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