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Simplifying Log(5x + 6) + log(3x + 2) = log(15x2 + 12x + 60) Reorder the terms: goL(6 + 5x) + log(3x + 2) = log(15x2 + 12x + 60) (6 * goL + 5x * goL) + log(3x + 2) = log(15x2 + 12x + 60) (6goL + 5goxL) + log(3x + 2) = log(15x2 + 12x + 60) Reorder the terms: 6goL + 5goxL + glo(2 + 3x) = log(15x2 + 12x + 60) 6goL + 5goxL + (2 * glo + 3x * glo) = log(15x2 + 12x + 60) 6goL + 5goxL + (2glo + 3glox) = log(15x2 + 12x + 60) Reorder the terms: 2glo + 3glox + 6goL + 5goxL = log(15x2 + 12x + 60) Reorder the terms: 2glo + 3glox + 6goL + 5goxL = glo(60 + 12x + 15x2) 2glo + 3glox + 6goL + 5goxL = (60 * glo + 12x * glo + 15x2 * glo) 2glo + 3glox + 6goL + 5goxL = (60glo + 12glox + 15glox2) Solving 2glo + 3glox + 6goL + 5goxL = 60glo + 12glox + 15glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-60glo' to each side of the equation. 2glo + 3glox + 6goL + -60glo + 5goxL = 60glo + 12glox + -60glo + 15glox2 Reorder the terms: 2glo + -60glo + 3glox + 6goL + 5goxL = 60glo + 12glox + -60glo + 15glox2 Combine like terms: 2glo + -60glo = -58glo -58glo + 3glox + 6goL + 5goxL = 60glo + 12glox + -60glo + 15glox2 Reorder the terms: -58glo + 3glox + 6goL + 5goxL = 60glo + -60glo + 12glox + 15glox2 Combine like terms: 60glo + -60glo = 0 -58glo + 3glox + 6goL + 5goxL = 0 + 12glox + 15glox2 -58glo + 3glox + 6goL + 5goxL = 12glox + 15glox2 Add '-12glox' to each side of the equation. -58glo + 3glox + 6goL + -12glox + 5goxL = 12glox + -12glox + 15glox2 Reorder the terms: -58glo + 3glox + -12glox + 6goL + 5goxL = 12glox + -12glox + 15glox2 Combine like terms: 3glox + -12glox = -9glox -58glo + -9glox + 6goL + 5goxL = 12glox + -12glox + 15glox2 Combine like terms: 12glox + -12glox = 0 -58glo + -9glox + 6goL + 5goxL = 0 + 15glox2 -58glo + -9glox + 6goL + 5goxL = 15glox2 Add '-15glox2' to each side of the equation. -58glo + -9glox + 6goL + -15glox2 + 5goxL = 15glox2 + -15glox2 Reorder the terms: -58glo + -9glox + -15glox2 + 6goL + 5goxL = 15glox2 + -15glox2 Combine like terms: 15glox2 + -15glox2 = 0 -58glo + -9glox + -15glox2 + 6goL + 5goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-58l + -9lx + -15lx2 + 6L + 5xL) = 0Subproblem 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 '(-58l + -9lx + -15lx2 + 6L + 5xL)' equal to zero and attempt to solve: Simplifying -58l + -9lx + -15lx2 + 6L + 5xL = 0 Reorder the terms: 6L + -58l + -9lx + -15lx2 + 5xL = 0 Solving 6L + -58l + -9lx + -15lx2 + 5xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + -58l + -9lx + -15lx2 + -6L + 5xL = 0 + -6L Reorder the terms: 6L + -6L + -58l + -9lx + -15lx2 + 5xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + -58l + -9lx + -15lx2 + 5xL = 0 + -6L -58l + -9lx + -15lx2 + 5xL = 0 + -6L Remove the zero: -58l + -9lx + -15lx2 + 5xL = -6L Add '58l' to each side of the equation. -58l + -9lx + -15lx2 + 58l + 5xL = -6L + 58l Reorder the terms: -58l + 58l + -9lx + -15lx2 + 5xL = -6L + 58l Combine like terms: -58l + 58l = 0 0 + -9lx + -15lx2 + 5xL = -6L + 58l -9lx + -15lx2 + 5xL = -6L + 58l Add '9lx' to each side of the equation. -9lx + -15lx2 + 9lx + 5xL = -6L + 58l + 9lx Reorder the terms: -9lx + 9lx + -15lx2 + 5xL = -6L + 58l + 9lx Combine like terms: -9lx + 9lx = 0 0 + -15lx2 + 5xL = -6L + 58l + 9lx -15lx2 + 5xL = -6L + 58l + 9lx Add '15lx2' to each side of the equation. -15lx2 + 15lx2 + 5xL = -6L + 58l + 9lx + 15lx2 Combine like terms: -15lx2 + 15lx2 = 0 0 + 5xL = -6L + 58l + 9lx + 15lx2 5xL = -6L + 58l + 9lx + 15lx2 Add '-5xL' to each side of the equation. 5xL + -5xL = -6L + 58l + 9lx + 15lx2 + -5xL Combine like terms: 5xL + -5xL = 0 0 = -6L + 58l + 9lx + 15lx2 + -5xL Simplifying 0 = -6L + 58l + 9lx + 15lx2 + -5xL 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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