Question

Please solve this question ❣️​

Answer 1

Answer:

$\color{red}{ \frac{5}{2} }$

Step-by-step explanation:

Your question:

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

Your answer:

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

[ reciprocal of (3/2)^-1

You must do the reciprocal if the power is negative in some cases ]

$( \frac{2}{3} ) ^{2x} \times \frac{2}{3} = ( \frac{2}{3} ) ^{ 3}$

[ now make roots of the squares ]

$( \frac{2}{3} ) ^{2x + 2} = ( \frac{2}{3} ) ^{3}$

[ since the LHS numbers are same so we mixed them by using this formula: (a/b)^m × (a/b)^n ]

$2x + 2 = 3$

[ now cancel 2/3 as they are same on both sides ]

$2x = 3 + 2$

[ do mathematical functions ]

$x = \frac{5}{2}$

Answer 2

$\large\bold{\underline{\underline{\purple{Here's\:your\:answer:-}}}}$

x = 1 (Answer)

$\large\bold{\underline{\underline{\red{❒ \: ꜱᴏʟᴜᴛɪᴏɴꜱ:-}}}}$

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

By Comparing power

$2x + 1 = 3 \\ \\ x = 1$

Happy Study !!