Question:
If $(27)^{x}=9 / 3^{x}$, find $x$
Solution:
We have,
$(27)^{x}=9 / 3^{x}$
$\left(3^{3 x}\right)^{x}=9 / 3^{x}$
$3^{3 x}=9 / 3^{x}$
$3^{3 x}=3^{2} / 3^{x}$
$3^{3 x}=3^{2-x}$
3x = 2 − x [On equating exponents]
3x + x = 2
4x = 2
x = 2/4
x = 1/2
Here the value of x is ½