Simplify: $log m + log m^{2} + log m^{3} + . . . + log m^{n}$

\frac{n (n + 1)}{2}

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\frac{m n}{2}

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\frac{n (n + 1)}{2} log m

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n (n + 1) log m^{2}

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Solution

The correct option is C $\frac{n (n + 1)}{2} log m$
$log m + log m^{2} + . . + log m^{n}$
As $log a^{b} = b log a$
$\Rightarrow log m + 2 log m + . . + n log m$
$\Rightarrow (1 + 2 + . . . + n) log m$
$\Rightarrow \frac{n (n + 1)}{2} log m$

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