Log[4](2x+8)=log[4](6x-12)

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Solution for Log[4](2x+8)=log[4](6x-12) equation:


Simplifying
Log[4](2x + 8) = log[4](6x + -12)

Reorder the terms:
goL * 4(8 + 2x) = log[4](6x + -12)

Reorder the terms for easier multiplication:
4goL(8 + 2x) = log[4](6x + -12)
(8 * 4goL + 2x * 4goL) = log[4](6x + -12)
(32goL + 8goxL) = log[4](6x + -12)

Reorder the terms:
32goL + 8goxL = glo * 4(-12 + 6x)

Reorder the terms for easier multiplication:
32goL + 8goxL = 4glo(-12 + 6x)
32goL + 8goxL = (-12 * 4glo + 6x * 4glo)
32goL + 8goxL = (-48glo + 24glox)

Solving
32goL + 8goxL = -48glo + 24glox

Solving for variable 'g'.

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

Add '48glo' to each side of the equation.
32goL + 48glo + 8goxL = -48glo + 48glo + 24glox

Reorder the terms:
48glo + 32goL + 8goxL = -48glo + 48glo + 24glox

Combine like terms: -48glo + 48glo = 0
48glo + 32goL + 8goxL = 0 + 24glox
48glo + 32goL + 8goxL = 24glox

Add '-24glox' to each side of the equation.
48glo + 32goL + -24glox + 8goxL = 24glox + -24glox

Reorder the terms:
48glo + -24glox + 32goL + 8goxL = 24glox + -24glox

Combine like terms: 24glox + -24glox = 0
48glo + -24glox + 32goL + 8goxL = 0

Factor out the Greatest Common Factor (GCF), '8go'.
8go(6l + -3lx + 4L + xL) = 0

Ignore the factor 8.

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 '(6l + -3lx + 4L + xL)' equal to zero and attempt to solve: Simplifying 6l + -3lx + 4L + xL = 0 Reorder the terms: 4L + 6l + -3lx + xL = 0 Solving 4L + 6l + -3lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + 6l + -3lx + -4L + xL = 0 + -4L Reorder the terms: 4L + -4L + 6l + -3lx + xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + 6l + -3lx + xL = 0 + -4L 6l + -3lx + xL = 0 + -4L Remove the zero: 6l + -3lx + xL = -4L Add '-6l' to each side of the equation. 6l + -3lx + -6l + xL = -4L + -6l Reorder the terms: 6l + -6l + -3lx + xL = -4L + -6l Combine like terms: 6l + -6l = 0 0 + -3lx + xL = -4L + -6l -3lx + xL = -4L + -6l Add '3lx' to each side of the equation. -3lx + 3lx + xL = -4L + -6l + 3lx Combine like terms: -3lx + 3lx = 0 0 + xL = -4L + -6l + 3lx xL = -4L + -6l + 3lx Add '-1xL' to each side of the equation. xL + -1xL = -4L + -6l + 3lx + -1xL Combine like terms: xL + -1xL = 0 0 = -4L + -6l + 3lx + -1xL Simplifying 0 = -4L + -6l + 3lx + -1xL 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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