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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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 =

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

227

Similar questions

, then x =

(a) 2
(b) 3
(c) 4
(d) 1

Q. Find

x

, if

{(\frac{2}{3})}^{x} {(\frac{3}{2})}^{2 x} = \frac{81}{16}

If $| x - 2 | = | x - 6 |$ then the value of $x$ is

If $\frac{1}{l o g_{3} π} + \frac{1}{l o g_{4} π} > x$ , then the biggest possible integer $x$ can take -

Q. If x sin 45° cos² 60° =

\frac{\tan^{2} 60 ° cosec 30 °}{\sec 45 ° \cot^{2 °} 30 °}

, then x =
(a) 2
(b) 4
(c) 8
(d) 16

Join BYJU'S Learning Program

If (23)x(32)2x=8116, then x =

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 =