Solve for x 4^(x^2+4x)=1/64

Problem

4(x2+4*x)=1/64

Solution

1. Rewrite the right side as a power of 4 by recognizing that 64=4

1/64=1/4

2. Apply the negative exponent rule to express the fraction as a base with a negative power.

1/4=4(−3)

3. Equate the exponents since the bases on both sides of the equation are now the same.

x2+4*x=−3

4. Set the quadratic equation to zero by adding 3 to both sides.

x2+4*x+3=0

5. Factor the quadratic expression by finding two numbers that multiply to 3 and add to 4.

(x+3)*(x+1)=0

6. Solve for x by setting each factor equal to zero using the zero product property.

x+3=0⇒x=−3

x+1=0⇒x=−1

Final Answer

x=−3,−1

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