Question

Find x if (2/3)x (3/2)2x =81/16

Answer 1

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Answer 2

Answer:

$Value \: of \: x = 4$

Step-by-step explanation:

$Given \: \left(\frac{2}{3}\right)^{x} \times \left(\frac{3}{2}\right)^{2x}=\frac{81}{16}$

$\implies \left(\frac{3}{2}\right)^{-x} \times \left(\frac{3}{2}\right)^{2x}=\frac{3^{4}}{2^{4}}$

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$By\: Exponential\:Law:\\</p><p>\boxed {\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^{n} }$

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$\implies \left(\frac{3}{2}\right)^{-x+2x}= \left(\frac{3}{2}\right)^{4}$

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$By\: Exponential\:Law:\\</p><p>\boxed {a^{m}\times a^{n}= a^{m+n}}$

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$\implies \left(\frac{3}{2}\right)^{x}= \left(\frac{3}{2}\right)^{4}$

$\implies x = 4$

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$\boxed {If \: a^m = a^{n}\implies m=n }$

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Therefore,

$Value \: of \: x = 4$

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