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Representation of Logarithmic Function

Express log 1...

Question

Express $l o g_{10} \sqrt[5]{108}$ in terms of $l o g_{10} 2$ and $l o g_{10} 3$

A

$\frac{1}{5} 2 l o g_{10} 2 + 3 l o g_{10} 3$

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B

$\frac{1}{5} 2 l o g_{10} 4 + 3 l o g_{10} 3$

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C

$\frac{1}{5} 2 l o g_{10} 2 + l o g_{10} 3$

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D

$\frac{1}{5} l o g_{10} 2 + 3 l o g_{10} 3$

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Solution

The correct option is A
$\frac{1}{5} 2 l o g_{10} 2 + 3 l o g_{10} 3$

$l o g_{10} \sqrt[5]{108}$ = $l o g_{10} (108)^{\frac{1}{5}}$

= $\frac{1}{5} l o g_{10} 108$

= $\frac{1}{5} l o g_{10} (2^{2} \times 3^{2})$

= $\frac{1}{5} l o g_{10} 2^{2} + l o g_{10} 3^{3}$

= $\frac{1}{5} 2 l o g_{10} 2 + 3 l o g_{10} 3$

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Similar questions

{log}_{10} \sqrt[5]{108}

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{log}_{10} 3

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{log}_{10} 3 = b

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