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If log8 p =...

Question

If ${log}_{8} p = 2.5$ and ${log}_{2} q = 5$ , then $p$ expressed in terms of $q$ is

A

p = q^{2}

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B

p = q^{8}

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C

p = q^{3 / 2}

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D

p = q^{5 / 2}

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E

p = q^{3}

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Solution

The correct option is A $p = q^{3 / 2}$
Given, ${log}_{8} p = 2.5$ and ${log}_{2} q = 5$
We have $p = 8^{2.5} = 2^{7.5}$ and $q = 2^{5}$
The relation between $p$ and $q$ is $p = q^{3 / 2}$ .

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