If ${log}_{2} (x^{3} + x^{2}) - {log}_{2} (x + 1) = 5$ , then ${log}_{2} x$ is:

\frac{5}{2}

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\frac{2}{5}

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5

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Solution

The correct option is B $\frac{5}{2}$
Given
${log}_{2} (x^{3} + x^{2}) - {log}_{2} (x + 1) = 5$

$\Rightarrow {log}_{2} \frac{x^{3} + x^{2}}{x + 1} = 5$

$\Rightarrow {log}_{2} x^{2} = 5$

$\Rightarrow 2 {log}_{2} x = 5$

$\Rightarrow {log}_{2} x = \frac{5}{2}$

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