Find the value of following - log 9 - 3- 3- 3

The correct option is A 716 Now, log _ 9 √( 3√( 3√( 3 ) #160; ) #160; ) #160; =log _ 3^2 √( 3√( 3× #160; 3^1/2 #160; ) #160; ) #16 ...

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Byju's Answer

Standard XI

Mathematics

Fundamental Laws of Logarithms

Find the valu...

Question

Find the value of following : ${log}_{9} \sqrt{3 \sqrt{3 \sqrt{3}}}$

\frac{7}{8}

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\frac{7}{16}

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\frac{1}{16}

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\frac{1}{8}

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Solution

The correct option is A $\frac{7}{16}$
Now,

${log}_{9} \sqrt{3 \sqrt{3 \sqrt{3}}}$

$= {log}_{3^{2}} \sqrt{3 \sqrt{3 \times 3^{\frac{1}{2}}}}$

$= \frac{1}{2} {log}_{3} \sqrt{3 \sqrt{3^{\frac{3}{2}}}}$

$= \frac{1}{2} {log}_{3} \sqrt{3 \times 3^{\frac{3}{4}}}$

$= \frac{1}{2} {log}_{3} \sqrt{3^{\frac{7}{4}}}$

$= \frac{1}{2} {log}_{3} 3^{\frac{7}{8}}$

$= \frac{1}{2} \times \frac{7}{8} \times {log}_{3} 3$

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

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Similar questions

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Q. Solve the following equations:

\frac{3 t + 1}{16} - \frac{2 t - 3}{7} = \frac{t + 3}{8} + \frac{3 t - 1}{14}

Find the missing number.

1, 8, 3, 16, 5, 32, 7,

, 9.

Q. Find variance of the following data.

Class interval	Frequency
$4 - 8$	$3$
$8 - 12$	$6$
$12 - 16$	$4$
$16 - 20$	$7$

Solve:

\frac{3 t + 1}{16} - \frac{2 t - 3}{7} = \frac{t + 3}{8} + \frac{3 t - 1}{14}

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Find the value of following : log9√3√3√3

The correct option is A 716Now,log9√3√3√3=log32√3√3×312=12log3√3√332=12log3√3×334=12log3√374=12log3378=12×78×log33=716.

Find the value of following : ${log}_{9} \sqrt{3 \sqrt{3 \sqrt{3}}}$