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

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve the equation 4^(x^2 - 4x) = 1/64

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

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

As the base is the same equate the exponents

x^2 - 4x = -3

=> x^2 - 4x + 3 = 0

=> x^2 - 3x - x + 3 = 0

=> x(x - 3) - 1(x - 3) = 0

=> (x - 1)(x - 3) = 0

x = 1 and x = 3

The solution is x = 1 and x = 3

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

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}.