Solution of equation 7x- 27 x-1-9261 where x- 2 and x is integer is divisible by

The correct option is D none of these 7^x(27^x 1)^1/x=9261 7^x(27)^x 1/x=9261 7^x(27)^x 1/x=7^3.(27)^1 Comparing exponents, gives us x=3 an ...

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Standard IX

Mathematics

Algebraic Identities

Solution of e...

Question

Solution of equation $(7^{x}) \sqrt[x]{{(27)}^{x - 1}} = 9261$ (where $x \geq 2$ and $x$ is integer) is divisible by

divisible by

2

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divisible by

3

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divisible by

6

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none of these

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Solution

The correct option is D none of these
$7^{x} (27^{x - 1})^{\frac{1}{x}} = 9261$
$7^{x} (27)^{\frac{x - 1}{x}} = 9261$
$7^{x} (27)^{\frac{x - 1}{x}} = 7^{3} . (27)^{1}$
Comparing exponents, gives us
$x = 3$ and $\frac{x - 1}{x} = 1$
$1 - \frac{1}{x} = 1$
$\frac{1}{x} = 0 . . . . (x \to \infty)$
Therefore there is no real value of x which satisfies the above equation.

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Similar questions

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Solution of equation (7x)x√(27)x−1=9261 (where x≥2 and x is integer) is divisible by

The correct option is D none of these7x(27x−1)1x=92617x(27)x−1x=92617x(27)x−1x=73.(27)1Comparing exponents, gives us x=3 and x−1x=11−1x=11x=0....(x→∞)Therefore there is no real value of x which satisfies the above equation.

Solution of equation $(7^{x}) \sqrt[x]{{(27)}^{x - 1}} = 9261$ (where $x \geq 2$ and $x$ is integer) is divisible by