If $3^{m} = 81$ $3^m=81$ , then what is #m^3?

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If $3^{m} = 81$ $3^m=81$ , then what is #m^3?

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Answer 1 · 2016-12-25T02:11:10

$64$ $64$

Explanation:

Sol. 1)
$81 = 3 \times 3 \times 3 \times 3 = 3^{4}$ $81=3xx3xx3xx3=3^4$
$3^{m} = 81, \Rightarrow 3^{4} = 81, \Rightarrow m = 4$ $3^m=81, => 3^4=81, => m=4$
$\Rightarrow m^{3} = 4^{3} = 4 \times 4 \times 4 = 64$ $=> m^3=4^3=4xx4xx4=64$

Sol.2) take log of both sides:
$3^{m} = 81$ $3^m=81$
$m log 3 = log 81$ $mlog3=log81$
$\Rightarrow m = \frac{log 81}{log 3} = 4$ $=> m=log81/log3=4$
$\Rightarrow m^{3} = 4^{3} = 4 \times 4 \times 4 = 64$ $=> m^3=4^3=4xx4xx4=64$

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