Question

find the value of x if (2/3)power x (3/2)power2x = 81/16

Answer 1

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Your answer
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$( \frac{2}{3} ) {}^{x} \times ( \frac{3}{2} ) {}^{2x} = \frac{81}{16} \\ \\ = > ( \frac{3}{2} ) {}^{ - x} \times ( \frac{3}{2} ) {}^{2x} = (\frac{3}{2} ) {}^{4} \\ \\ = > ( \frac{3}{2} ) {}^{2x - x} = ( \frac{3}{2} ) {}^{4} \\ \\ = > ( \frac{3}{2} ) {}^{x} = ( \frac{3}{2} ) {}^{4} \\ \\ on \: equalising \: the \: exponents \: of \: both \: sides \: we \: get \: \\ \\ = > x = 4$
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Answer 2

Here is your answer

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