If -3n-729- then the value of n is-

The correct option is C 12 √(3^n) = 729 = 3^6⇔( √(3^n))^2 = ( 3^6)^2⇔3^n = 3^12⇔ n = 12. ...

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Standard VII

Mathematics

Power Law

If √3n=729, t...

Question

If $\sqrt{3^{n}} = 729$ , then the value of $^{'} n^{'}$ is?

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Solution

The correct option is C: 12
$\sqrt{3^{n}} = 729 = 3^{6}$
$\Rightarrow {(\sqrt{3^{n}})}^{2} = {(3^{6})}^{2}$ [Squaring both sides]
$\Rightarrow 3^{n} = 3^{12}$ [ $∵ (a^{n})^{m} = a^{m \times n}$ ]
$\Rightarrow n = 12$ [When base is same on both sides of equation, then exponents will be equal]

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If √3n=729, then the value of ′n′ is?

The correct option is C: 12√3n=729=36⇒(√3n)2=(36)2 [Squaring both sides] ⇒3n=312 [∵(an)m=am×n] ⇒n=12 [When base is same on both sides of equation, then exponents will be equal]

If $\sqrt{3^{n}} = 729$ , then the value of $^{'} n^{'}$ is?

The correct option is C: 12
$\sqrt{3^{n}} = 729 = 3^{6}$
$\Rightarrow {(\sqrt{3^{n}})}^{2} = {(3^{6})}^{2}$ [Squaring both sides]
$\Rightarrow 3^{n} = 3^{12}$ [ $∵ (a^{n})^{m} = a^{m \times n}$ ]
$\Rightarrow n = 12$ [When base is same on both sides of equation, then exponents will be equal]