Log[5](6x-4)=log[5](x^2-20)

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Solution for Log[5](6x-4)=log[5](x^2-20) equation:


Simplifying
Log[5](6x + -4) = log[5](x2 + -20)

Reorder the terms:
goL * 5(-4 + 6x) = log[5](x2 + -20)

Reorder the terms for easier multiplication:
5goL(-4 + 6x) = log[5](x2 + -20)
(-4 * 5goL + 6x * 5goL) = log[5](x2 + -20)
(-20goL + 30goxL) = log[5](x2 + -20)

Reorder the terms:
-20goL + 30goxL = glo * 5(-20 + x2)

Reorder the terms for easier multiplication:
-20goL + 30goxL = 5glo(-20 + x2)
-20goL + 30goxL = (-20 * 5glo + x2 * 5glo)
-20goL + 30goxL = (-100glo + 5glox2)

Solving
-20goL + 30goxL = -100glo + 5glox2

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '100glo' to each side of the equation.
-20goL + 100glo + 30goxL = -100glo + 100glo + 5glox2

Reorder the terms:
100glo + -20goL + 30goxL = -100glo + 100glo + 5glox2

Combine like terms: -100glo + 100glo = 0
100glo + -20goL + 30goxL = 0 + 5glox2
100glo + -20goL + 30goxL = 5glox2

Add '-5glox2' to each side of the equation.
100glo + -20goL + -5glox2 + 30goxL = 5glox2 + -5glox2

Reorder the terms:
100glo + -5glox2 + -20goL + 30goxL = 5glox2 + -5glox2

Combine like terms: 5glox2 + -5glox2 = 0
100glo + -5glox2 + -20goL + 30goxL = 0

Factor out the Greatest Common Factor (GCF), '5go'.
5go(20l + -1lx2 + -4L + 6xL) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(20l + -1lx2 + -4L + 6xL)' equal to zero and attempt to solve: Simplifying 20l + -1lx2 + -4L + 6xL = 0 Reorder the terms: -4L + 20l + -1lx2 + 6xL = 0 Solving -4L + 20l + -1lx2 + 6xL = 0 Move all terms containing g to the left, all other terms to the right. Add '4L' to each side of the equation. -4L + 20l + -1lx2 + 4L + 6xL = 0 + 4L Reorder the terms: -4L + 4L + 20l + -1lx2 + 6xL = 0 + 4L Combine like terms: -4L + 4L = 0 0 + 20l + -1lx2 + 6xL = 0 + 4L 20l + -1lx2 + 6xL = 0 + 4L Remove the zero: 20l + -1lx2 + 6xL = 4L Add '-20l' to each side of the equation. 20l + -1lx2 + -20l + 6xL = 4L + -20l Reorder the terms: 20l + -20l + -1lx2 + 6xL = 4L + -20l Combine like terms: 20l + -20l = 0 0 + -1lx2 + 6xL = 4L + -20l -1lx2 + 6xL = 4L + -20l Add 'lx2' to each side of the equation. -1lx2 + lx2 + 6xL = 4L + -20l + lx2 Combine like terms: -1lx2 + lx2 = 0 0 + 6xL = 4L + -20l + lx2 6xL = 4L + -20l + lx2 Add '-6xL' to each side of the equation. 6xL + -6xL = 4L + -20l + lx2 + -6xL Combine like terms: 6xL + -6xL = 0 0 = 4L + -20l + lx2 + -6xL Simplifying 0 = 4L + -20l + lx2 + -6xL The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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