Question

$log \sqrt{3 \sqrt{3 \sqrt{3 \: \: \: \:to \: the \: base \: 9} } }$
please answer​

Answer 1

Question :-

$log_{9} \ \ \sqrt{3 \sqrt{3 \sqrt{3} } }$

SOLUTION :-

Given

$log_{9} \: \: \sqrt{3 \sqrt{3 \sqrt{3} } }$

$= > log_{9} \sqrt{3 \sqrt{3 \times {3}^{ \frac{1}{2} } } }$

$= > log_{9} \sqrt{3 \sqrt{ {3}^{ \frac{3}{2} } } }$

$= > log_{ {3}^{2} } \sqrt{3 \times {3}^{ \frac{3}{4} } }$

$= > log_{ {3}^{2} } \: \: \: \: {3}^{ \frac{7}{8} }$

$= > \frac{1}{2} \times \frac{7}{8} \: \: \: log_{ {3}^{3} }$

$= > \frac{7}{16} \times 1$

$= > \frac{7}{16}$

Therefore ,

$\pink{ \frac{7}{16} }\: is \: \: the \: \: ans$

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Answer 2

Step-by-step explanation:

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