Question

find log1728 to the base2√3

Answer 1

Answer:

6

Step-by-step explanation:

Here,

$1728 = 2 \times 864 \\ = 2 \times 2 \times 432 \\ = 2 \times 2 \times 2 \times 216 \\ = 2 \times 2 \times 2 \times 2 \times 108 \\ = 2 \times 2 \times 2 \times 2 \times 2 \times 54 \\ 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 7 \\ = {2}^{6} \times {3}^{3 } \\ = {2}^{6} \times ({ \sqrt{3} })^{2 \times 3} \\ = {2}^{6} \times ({ \sqrt{3} })^{6} \\ 1728 = {(2 \times \sqrt{3} )}^{6}$

Now,

$log_{2 \sqrt{3} }(1728) = log_{2 \sqrt{3} }( {(2 \sqrt{3}) }^{6} ) \\ = 6 \times log_{2 \sqrt{3} }(2 \sqrt{3} ) \\ = 6 \times 1 \\ = 6$

I hope this might help you.

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