Evaluate the solutions of the equation 4^(x^2-4x)=1/64

This is an exponential
equation.

For the beginning, we'll write 1/64 =
1/4^3

We'll apply the property of negative
power:

1/4^3 = 4^(-3)

Now,
we'll re-write the equation:

4^(x^2-4x) =
1/64

4^(x^2-4x) = 4^(-3)

Since
the bases are matching, we'll apply one to one
property:

x^2-4x = -3

We'll
add 3 both sides:

x^2-4x+3 =
0

According to the rule, the quadratic equation could be
written as:

x^2 - Sx + P =
0

From Viete's relations, we'll
get:

S = x1 + x2

x1 + x2 =
4

x1*x2 = 3

x1 =
1

x2 =
3

The solutions of the
equation are :{1 ; 3}.