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Simplifying Log(7)(4x + 4) + log(7)(x + -3) = 2log(7)(2x + -3) Reorder the terms: goL * 7(4 + 4x) + log(7)(x + -3) = 2log(7)(2x + -3) Reorder the terms for easier multiplication: 7goL(4 + 4x) + log(7)(x + -3) = 2log(7)(2x + -3) (4 * 7goL + 4x * 7goL) + log(7)(x + -3) = 2log(7)(2x + -3) (28goL + 28goxL) + log(7)(x + -3) = 2log(7)(2x + -3) Reorder the terms: 28goL + 28goxL + glo * 7(-3 + x) = 2log(7)(2x + -3) Reorder the terms for easier multiplication: 28goL + 28goxL + 7glo(-3 + x) = 2log(7)(2x + -3) 28goL + 28goxL + (-3 * 7glo + x * 7glo) = 2log(7)(2x + -3) 28goL + 28goxL + (-21glo + 7glox) = 2log(7)(2x + -3) Reorder the terms: -21glo + 7glox + 28goL + 28goxL = 2log(7)(2x + -3) Reorder the terms: -21glo + 7glox + 28goL + 28goxL = 2glo * 7(-3 + 2x) Reorder the terms for easier multiplication: -21glo + 7glox + 28goL + 28goxL = 2 * 7glo(-3 + 2x) Multiply 2 * 7 -21glo + 7glox + 28goL + 28goxL = 14glo(-3 + 2x) -21glo + 7glox + 28goL + 28goxL = (-3 * 14glo + 2x * 14glo) -21glo + 7glox + 28goL + 28goxL = (-42glo + 28glox) Solving -21glo + 7glox + 28goL + 28goxL = -42glo + 28glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '42glo' to each side of the equation. -21glo + 7glox + 28goL + 42glo + 28goxL = -42glo + 42glo + 28glox Reorder the terms: -21glo + 42glo + 7glox + 28goL + 28goxL = -42glo + 42glo + 28glox Combine like terms: -21glo + 42glo = 21glo 21glo + 7glox + 28goL + 28goxL = -42glo + 42glo + 28glox Combine like terms: -42glo + 42glo = 0 21glo + 7glox + 28goL + 28goxL = 0 + 28glox 21glo + 7glox + 28goL + 28goxL = 28glox Add '-28glox' to each side of the equation. 21glo + 7glox + 28goL + -28glox + 28goxL = 28glox + -28glox Reorder the terms: 21glo + 7glox + -28glox + 28goL + 28goxL = 28glox + -28glox Combine like terms: 7glox + -28glox = -21glox 21glo + -21glox + 28goL + 28goxL = 28glox + -28glox Combine like terms: 28glox + -28glox = 0 21glo + -21glox + 28goL + 28goxL = 0 Factor out the Greatest Common Factor (GCF), '7go'. 7go(3l + -3lx + 4L + 4xL) = 0 Ignore the factor 7.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 '(3l + -3lx + 4L + 4xL)' equal to zero and attempt to solve: Simplifying 3l + -3lx + 4L + 4xL = 0 Reorder the terms: 4L + 3l + -3lx + 4xL = 0 Solving 4L + 3l + -3lx + 4xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + 3l + -3lx + -4L + 4xL = 0 + -4L Reorder the terms: 4L + -4L + 3l + -3lx + 4xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + 3l + -3lx + 4xL = 0 + -4L 3l + -3lx + 4xL = 0 + -4L Remove the zero: 3l + -3lx + 4xL = -4L Add '-3l' to each side of the equation. 3l + -3lx + -3l + 4xL = -4L + -3l Reorder the terms: 3l + -3l + -3lx + 4xL = -4L + -3l Combine like terms: 3l + -3l = 0 0 + -3lx + 4xL = -4L + -3l -3lx + 4xL = -4L + -3l Add '3lx' to each side of the equation. -3lx + 3lx + 4xL = -4L + -3l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 4xL = -4L + -3l + 3lx 4xL = -4L + -3l + 3lx Add '-4xL' to each side of the equation. 4xL + -4xL = -4L + -3l + 3lx + -4xL Combine like terms: 4xL + -4xL = 0 0 = -4L + -3l + 3lx + -4xL Simplifying 0 = -4L + -3l + 3lx + -4xL 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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