Question

If 27^x=9/3^x ,then the value of x is

Answer 1

x = 0.5

Explanation:

Well, we have in this case a exponent equation

`27^(x) = (9)/(3^(x))`

Factoring 27 =
`3^(3)`

Our new equation is:

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

Applying the property of exponents, on the right we'll have just like that:

`3^(3x) = 3^(2-x)`

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