Download If , find all values of x such that f(x) = 256

x 2 3 x
If f ( x)  4
, find all values of x such that f(x) = 256.
Solution: Since f(x)=256, we can plug in 256 for f(x) in the first equation to get.
256  4 x 3 x
We need to write both sides of the equation as powers of the same base so we ask: 4 raised to
what power is 256?
2
44  4 x
2
3 x
Once the bases are the same, we know the exponents must be equal:
4 = x2 + 3x
To solve a quadratic equation, we need one side of the equation to be zero, so we subtract 4 from
both sides:
x2 + 3x – 4 = 0
Factoring:
(x + 4)(x – 1) = 0
Setting each factor equal to zero:
x + 4 = 0 or x – 1 = 0
x = - 4 or x = 1