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

Problem

4(x−x2)=1/64

Solution

1. Rewrite the base on the right side of the equation so that both sides have a common base of 4 Since 64=4 we can substitute this into the expression.

64=(4)x

2. Apply exponent rules to simplify the right side. Use the power of a power rule (am)n=a(m*n) and the negative exponent rule 1/(an)=a(−n)

1/((4)x)=1/(4(3*x))

1/(4(3*x))=4(−3*x)

3. Equate the exponents because the bases are now identical. If bm=bn then m=n

x−x2=−3*x

4. Rearrange the equation into a standard quadratic form a*x2+b*x+c=0 by moving all terms to one side.

−x2+x+3*x=0

−x2+4*x=0

5. Factor the quadratic expression to find the roots.

−x*(x−4)=0

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

−x=0⇒x=0

x−4=0⇒x=4

Final Answer

x=0,4

Want more problems? Check here!