Math, asked by mayankrajdav, 1 year ago

Find x . (-3/2)^6 * (4/9)^3 = (1/2)^3x

Answers

Answered by mysticd
94

Answer:

Value of x = 0

Step-by-step explanation:

\left(\frac{-3}{2}\right)^{6}\times \left(\frac{4}{9}\right)^{3}= \left(\frac{1}{2}\right)^{3x}

\implies \left(\frac{-3}{2}\right)^{6}\times \left(\frac{2^{2}}{3^{2}}\right)^{3}= \left(\frac{1}{2}\right)^{3x}

\implies \left(\frac{3}{2}\right)^{6}\times \left(\frac{2}{3}\right)^{2\times 3}= \left(\frac{1}{2}\right)^{3x}

\implies \left( \frac{3}{2}\times \frac{2}{3}\right)^{6}=\left(\frac{1}{2}\right)^{3x}

\implies 1^{6} =\left(\frac{1}{2}\right)^{3x}

 \implies 1 = \left(\frac{1}{2}\right)^{3x}

 \implies \left(\frac{1}{2}\right)^{0}=\left(\frac{1}{2}\right)^{3x}

 Since, \boxed { a^{0} = 1 }

\implies 0 = 3x

 Since, \boxed { If \: a^{m} = a^{n} \: then \: m=n }

 \implies x = 0

Therefore.,

Value of x = 0

•••♪

Answered by srijanpal47
26

Answer:

(-3/2)6 * (4/9)3 = (1/2)3x

(-3/2)6 * {(2)2/(3)2}3 = (1/2)3x

(-3/2)6 * (2/3)3*2 = (1/2)3x

(-3/2)6 * (2/3)6 = (1/2)3x

{(-3/2)*(2/3)}6 = (1/2)3x

(-1)6 = (1/2)3x

1 = 1/23x

23x = 1

8x = 1

=> x = 0

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