Question

1. If 81^x = 9/3^x, find 'x'.
2. Find the value of√3^-2.
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Answer 1

Answer:

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Answer 2

$HEYA \: \\ \\ 1) \: \: \: \: (81) {}^{x} = 9 \times 3 {}^{ - x} \\ \\ 3 {}^{4x} = 3 {}^{2} \times 3 {}^{ - x} \\ \\ 3 {}^{4x} = 3 {}^{2 - x} \\ \\ now \: compare \: powers \: of \: 3 \: we \: have \\ \\ 4x = 2 - x \\ \\ 5x = 2 \\ \\ x = 2\div 5 \\ \\ 2) \: \: ( \sqrt{3} ) {}^{ - 2} \\ \\ (3) {}^{(1 \div 2) \times - 2} \\ \\ 3 {}^{ - 1} \\ \\ = 1 \div 3$