If 2-3 x 3-2 2x-81-16- then x - 2431

The correct option is B 4 (2/3 )^x (3/2 )^2x=81/16 ⇒(3/2 )^ x× (3/2 )^2x = 3^4/2^4=(3/2 )^4 ⇒(3/2 )^2x x = (3/2 )^4⇒(3/2 )^x=(3/2 )^4 Comparing, we get x = 4 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

If 2/3 x 3/2 ...

Question

If ${(\frac{2}{3})}^{x} {(\frac{3}{2})}^{2 x} = \frac{81}{16}$ , then x =

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Solution

The correct option is C
4

${(\frac{2}{3})}^{x} {(\frac{3}{2})}^{2 x} = \frac{81}{16} \Rightarrow {(\frac{3}{2})}^{- x} \times {(\frac{3}{2})}^{2 x} = \frac{3^{4}}{2^{4}} = {(\frac{3}{2})}^{4} \Rightarrow {(\frac{3}{2})}^{2 x - x} = {(\frac{3}{2})}^{4} \Rightarrow {(\frac{3}{2})}^{x} = {(\frac{3}{2})}^{4}$

Comparing, we get x = 4

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The correct option is C 4 (23)x(32)2x=8116⇒(32)−x×(32)2x=3424=(32)4⇒(32)2x−x=(32)4⇒(32)x=(32)4 Comparing, we get x = 4

If ${(\frac{2}{3})}^{x} {(\frac{3}{2})}^{2 x} = \frac{81}{16}$ , then x =