Question

please help me out with answering​

Answer 1

Answer:

X = 4

Step-by-step explanation:

$( \frac{9}{4} ){}^{x} \times (\frac{8}{27} ) {}^{x - 1} = \frac{2}{3} \\ \\ (\frac{2}{3} ) {}^{ - 2x} \times ( \frac{2}{3} ) {}^{3(x - 1)} = \frac{2}{3} \\ \\ ( \frac{2}{3} ) {}^{ - 2x + 3x - 3} = \frac{2}{3} \\ \\ x - 3 = 1 \\ \\ therefore \: \\ \\ x = 4.$

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Answer 2

Answer:

x = 4

Step-by-step explanation:

${( \frac{9}{4}) }^{x} \times { (\frac{8}{27}) }^{x - 1} = \frac{2}{3} \\ = > {( \frac{3}{2}) }^{2x} \times { (\frac{2}{3}) }^{3x - 3} = \frac{2}{3} \\ = > {( \frac{2}{3}) }^{ - 2x} \times { (\frac{2}{3}) }^{3x - 3} = \frac{2}{3} \\ = > { (\frac{2}{3}) }^{ - 2x + 3x - 3} = { (\frac{2}{3}) }^{1} \\ = > x - 3 = 1 \\ = > x = 4$

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