Question

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

Answer 1

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

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Answer 2

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