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Comparision of Quantities Using Exponents

Solve: 9× 81...

Question

Solve:
$9 \times 81^{x} = 27^{2 - x}$

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Solution

$9 \times 81^{x} = 27^{2 - x} 3^{2} \times 3^{4 x} = 3^{6 - 3 x} 3^{2 + 4 x} = 3^{6 - 3 x}$
Equating powers
$2 + 4 x = 6 - 3 x 7 x = 4 x = \frac{4}{7}$

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Comparision of Quantities Using Exponents

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