If log x-b-c-log y-c-a-log z-a-b then xa- yb- zc-

The correct option is B xyz Let t=x^ay^bz^c, then log t=∑ a log x=∑ ak(b c)=0 ∴ t=x^ay^bz^c=1 Again ∑ log x=∑ k(b c)=0 log xyz=0 or xyz=1 ∴ x^ay^bz^c=1=xyz ...

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Byju's Answer

Standard IX

Mathematics

Property 1

If log x/b-c=...

Question

If $\frac{l o g x}{b - c} = \frac{l o g y}{c - a} = \frac{l o g z}{a - b}$ then $x^{a} . y^{b} . z^{c} =$

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abc

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xyz

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None of these

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Solution

The correct option is C
xyz

Let $t = x^{a} y^{b} z^{c}$ , then
$l o g t = \sum a l o g x = \sum a k (b - c) = 0$
$∴ t = x^{a} y^{b} z^{c} = 1$
Again $\sum l o g x = \sum k (b - c) = 0$
$l o g x y z = 0$ or $x y z = 1$
$∴ x^{a} y^{b} z^{c} = 1 = x y z$

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If log xb−c=log yc−a=log za−b then xa.yb.zc=

The correct option is C xyz Let t=xaybzc, then log t=∑a log x=∑ ak(b−c)=0 ∴ t=xaybzc=1 Again ∑log x=∑k(b−c)=0 log xyz=0 or xyz=1 ∴ xaybzc=1=xyz

If $\frac{l o g x}{b - c} = \frac{l o g y}{c - a} = \frac{l o g z}{a - b}$ then $x^{a} . y^{b} . z^{c} =$

The correct option is C
xyz

Let $t = x^{a} y^{b} z^{c}$ , then
$l o g t = \sum a l o g x = \sum a k (b - c) = 0$
$∴ t = x^{a} y^{b} z^{c} = 1$
Again $\sum l o g x = \sum k (b - c) = 0$
$l o g x y z = 0$ or $x y z = 1$
$∴ x^{a} y^{b} z^{c} = 1 = x y z$