If - 3- 3- 3- 3- 3 - 3 n- find the value of n-

The correct option is D 3132 √(3√(3√(3√(3√(3)))))=3^n ⇒√(3√(3√(3√(3^(32))))) ⇒√(3)√(3√(3^(74))) ⇒√(3√(3^(158))) ⇒√(3^(3116)) ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Laws of Logarithms

If √ 3√ 3√ ...

Question

If $\sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3}}}}} = 3^{n}$ , find the value of $n$ .

\frac{11}{24}

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\frac{15}{16}

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\frac{63}{64}

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\frac{31}{32}

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Solution

The correct option is D $\frac{31}{32}$
$\sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3}}}}} = 3^{n}$

$\Rightarrow \sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3^{(\frac{3}{2})}}}}}$

$\Rightarrow \sqrt{3} \sqrt{3 \sqrt{3^{(\frac{7}{4})}}}$

$\Rightarrow \sqrt{3 \sqrt{3^{(\frac{15}{8})}}}$

$\Rightarrow \sqrt{3^{(\frac{31}{16})}}$

$\Rightarrow 3^{(\frac{31}{32})} \Rightarrow n = \frac{31}{32}$ .

Therefore, option $D$ is correct.

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If √3√3√3√3√3=3n, find the value of n.

The correct option is D 3132√3√3√3√3√3=3n⇒ ⎷3√3√3√3(32)⇒√3√3√3(74)⇒√3√3(158)⇒√3(3116)⇒3(3132)⇒n=3132.Therefore, option D is correct.

If $\sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3}}}}} = 3^{n}$ , find the value of $n$ .