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Property 2

If log yx=1...

Question

If ${log}_{y} x = 10$ then ${log}_{x^{3}} (y^{6})$ is equal to

A

5

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B

\frac{1}{5}

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C

6

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D

\frac{1}{6}

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Solution

The correct option is B $\frac{1}{5}$
${log}_{y} x = 10$
$∴ {log}_{x^{3}} (y^{6}) = 6. {log}_{x^{3}} y$
$= \frac{6}{3} {log}_{x} y = 2. {log}_{x} y$
$= 2. \frac{1}{{log}_{y} x} = \frac{2}{10} = \frac{1}{5}$

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