Answer:
x = 0.5
Step-by-step explanation:
Well, we have in this case a exponent equation
[tex]27^{x} = \frac{9}{3^{x}}[/tex]
Factoring 27 = [tex]3^{3}[/tex]
Our new equation is:
[tex]3^{3x}=\frac{3^{2}}{3^{x}}[/tex]
Applying the property of exponents, on the right we'll have just like that:
[tex]3^{3x} = 3^{2-x}[/tex]
now, it's easy to solve this equation. You must solve 3x = 2 - x because the basis of these exponents are equal.
3x = 2 - x
3x + x = 2
4x = 2
x = 1/2 or 0.5
