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If  (97)3×(4981)2x−6=(79)9,\left(\frac{9}{7}\right)^3 \times \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^9,(79)3×(8149)2x−6=

Question

If $\left(\frac{9}{7}\right)^3 \times \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^9,$ then value of x is -

9

6

8

12

Solution

Correct option is B

Given:

\left(\frac{9}{7}\right)^3 \times \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^9

Formula used:

a^m \times a^n = a^{m + n}

Solution:

\frac{49}{81} = \frac{7^2}{9^2} = \left(\frac{7}{9}\right)^2 \\\Rightarrow \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^{4x - 12} \\Also, \left(\frac{9}{7}\right)^3 = \left(\frac{7}{9}\right)^{-3}

So,

\left(\frac{7}{9}\right)^{-3} \times \left(\frac{7}{9}\right)^{4x - 12} = \left(\frac{7}{9}\right)^9 \\\Rightarrow \left(\frac{7}{9}\right)^{4x - 15} = \left(\frac{7}{9}\right)^9

Equating powers:
4x - 15 = 9

\Rightarrow 4x = 24 \\\Rightarrow x = 6

Correct answer is (b) 6

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If $\left(\frac{9}{7}\right)^3 \times \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^9,$ then value of x is -

9

6

8

12

Correct option is B

Free Tests

UPTET : Paper 1 Full Mock - 01

UPTET : Paper 2 Maths & Science Full Mock - 01

UPTET : Paper 2 Social Science Full Mock - 01

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If (97)3×(4981)2x−6=(79)9,\left(\frac{9}{7}\right)^3 \times \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^9,(79​)3×(8149​)2x−6=(97​)9, then value of x is -

9

6

8

12

Correct option is B

Free Tests

UPTET : Paper 1 Full Mock - 01

UPTET : Paper 2 Maths & Science Full Mock - 01

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If $\left(\frac{9}{7}\right)^3 \times \left(\frac{49}{81}\right)^{2x - 6} = \left(\frac{7}{9}\right)^9,$ then value of x is -