Solve 3 x 2- 32 x -27- 1A- 1-41919 - 1012 mB- x -1-1- x -3-1D- x-3-2

The correct options are A 1.41919x1012 mGiven 3^x^2 : 3^2x = 27 : 1 ⇒ 3^x^2/3^2x = 27/1 ⇒ 3^x^2 = 27 × 3^2x ⇒ 3^x^2 = 3^3 × 3^2x ⇒ 3^x^2 = 3^3+2x Equating t ...

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Byju's Answer

Standard IX

Mathematics

Product Law

Solve 3 x 2: ...

Question

Solve

$3^{x^{2}} : 3^{2 x} = 27 : 1$

1.41919x1012 m

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$x = 1, - 1$

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$x = 3, 1$

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$x = 3, - 2$

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Solution

The correct option is A 1.41919x1012 m
Given

$3^{x^{2}} : 3^{2 x} = 27 : 1$

$\Rightarrow$ $\frac{3^{x^{2}}}{3^{2 x}} = \frac{27}{1}$

$\Rightarrow$ $3^{x^{2}} = 27 \times 3^{2 x}$

$\Rightarrow$ $3^{x^{2}} = 3^{3} \times 3^{2 x}$

$\Rightarrow$ $3^{x^{2}} = 3^{3 + 2 x}$

Equating the powers

$x^{2} = 3 + 2 x$

$x^{2} - 2 x - 3 = 0$

Solving this we get

$x = 3, - 1$

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Solve 3x2:32x = 27:1

The correct option is A 1.41919x1012 mGiven 3x2:32x = 27:1 ⇒ 3x232x = 271 ⇒ 3x2 = 27×32x ⇒ 3x2 = 33×32x ⇒ 3x2 = 33+2x Equating the powers x2=3+2x x2−2x−3=0 Solving this we get x=3,−1

Solve

$3^{x^{2}} : 3^{2 x} = 27 : 1$