The value of the logarithmic function $(b^{2})^{5 {log}_{b} x}$ is:

10^{x}

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x^{4}

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10 x

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x^{10}

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Solution

The correct option is D $x^{10}$
Consider, $(b^{2})^{5 {log}_{b} x} = b^{10 {log}_{b} x}$

$= b^{{log}_{b} (x)^{10}} (b^{{log}_{b} (x)^{n}} = x^{n})$

$= x^{10}$

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