Question

find the value of x so that (3/4)^9×(3/4)^-7=(3/4)^4x​

Answer 1

$\textbf{Given:}$

$(\dfrac{3}{4})^9{\times}(\dfrac{3}{4})^{-7}=(\dfrac{3}{4})^{4x}$

$\textbf{To find:}$

$\text{The value of x}$

$\textbf{Solution:}$

$\text{Consider,}$

$(\dfrac{3}{4})^9{\times}(\dfrac{3}{4})^{-7}=(\dfrac{3}{4})^{4x}$

$\text{Using,}$

$\boxed{\bf\,a^m{\times}a^n=a^{m+n}}$

$(\dfrac{3}{4})^{9+(-7)}=(\dfrac{3}{4})^{4x}$

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

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

$4x=2$

$\implies\,x=\dfrac{2}{4}$

$\implies\boxed{\bf\,x=\dfrac{1}{2}}$

Answer 2

this is right answer ok