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Simplifying log(6)(3x + -10) = log(6)(14 + -5x) Reorder the terms: glo * 6(-10 + 3x) = log(6)(14 + -5x) Reorder the terms for easier multiplication: 6glo(-10 + 3x) = log(6)(14 + -5x) (-10 * 6glo + 3x * 6glo) = log(6)(14 + -5x) (-60glo + 18glox) = log(6)(14 + -5x) Reorder the terms for easier multiplication: -60glo + 18glox = 6glo(14 + -5x) -60glo + 18glox = (14 * 6glo + -5x * 6glo) -60glo + 18glox = (84glo + -30glox) Solving -60glo + 18glox = 84glo + -30glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-84glo' to each side of the equation. -60glo + -84glo + 18glox = 84glo + -84glo + -30glox Combine like terms: -60glo + -84glo = -144glo -144glo + 18glox = 84glo + -84glo + -30glox Combine like terms: 84glo + -84glo = 0 -144glo + 18glox = 0 + -30glox -144glo + 18glox = -30glox Add '30glox' to each side of the equation. -144glo + 18glox + 30glox = -30glox + 30glox Combine like terms: 18glox + 30glox = 48glox -144glo + 48glox = -30glox + 30glox Combine like terms: -30glox + 30glox = 0 -144glo + 48glox = 0 Factor out the Greatest Common Factor (GCF), '48glo'. 48glo(-3 + x) = 0 Ignore the factor 48.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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