( 2 3 ) X ( 3 2 ) 2 X = 81 16 Then X = - Mathematics

MCQ

(2/3)^x (3/2)^(2x)=81/16 then x

• 2

• 3

• 4

• 1

Solution

We have to find value of x  provided  (2/3)^x (3/2)^(2x)=81/16

So,

(2/3)^x (3/2)^(2x)=81/16

(2/3)^x (3/2)^(2x)= 3^4/3^4

(2x)/(3x) (3^(2x))/(2^(2x)) = 3^4/2^4

3^(2x -x)/2^(2x-x) = 3^4/2^4

3^x/2^x = 3^4/2^4

Equating exponents of power we get x = 4.

Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 15 | Page 30