Question

Find x if( 2/3)^x ×(3/2)^2x=81/16

Answer 1

$\textbf{Given:}$

$\mathsf{\left(\dfrac{2}{3}\right)^x{\times}\left(\dfrac{3}{2}\right)^{2x}=\dfrac{81}{16}}$

$\textbf{To find:}$

$\textsf{The value of x}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{\left(\dfrac{2}{3}\right)^x{\times}\left(\dfrac{3}{2}\right)^{2x}=\dfrac{81}{16}}$

$\mathsf{\dfrac{2^x}{3^x}{\times}\dfrac{3^{2x}}{2^{2x}}=\dfrac{81}{16}}$

$\mathsf{\dfrac{3^{2x-x}}{2^{2x-x}}=\dfrac{81}{16}}$

$\mathsf{\dfrac{3^x}{2^x}=\dfrac{3^4}{2^4}}$

$\mathsf{\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^4}$

$\textsf{Equating powers on bothsides, we get}$

$\mathsf{x=4}$

$\textbf{Answer:}$

$\textsf{The value of x is 4}$

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Answer 2

Answer:

step by step explanation

We are provided that (2/3)^x * (3/2)^2x = 81/16

so at first let us write (2/3)^x as (3/2)^-x , to collaborate with 81/16 as 3^4/2^4

so let's do the process

or. (3/2)^-x * (3/2)^2x = 3^4/2^4

or. (3/2)^-x + 2x = (3/2)^4

so as on the both side of equal sign it have the same base. Thus we can remove the base and equate only with their exponent

so.

or. -x+2x =4

by subtracting -x and 2x we get only x

so

or. x = 4

so the value of x is 4

Hope this will help you. Thank you for reading this