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Simplifying log(3)(6x + -8) = log(3)(5x + 10) Reorder the terms: glo * 3(-8 + 6x) = log(3)(5x + 10) Reorder the terms for easier multiplication: 3glo(-8 + 6x) = log(3)(5x + 10) (-8 * 3glo + 6x * 3glo) = log(3)(5x + 10) (-24glo + 18glox) = log(3)(5x + 10) Reorder the terms: -24glo + 18glox = glo * 3(10 + 5x) Reorder the terms for easier multiplication: -24glo + 18glox = 3glo(10 + 5x) -24glo + 18glox = (10 * 3glo + 5x * 3glo) -24glo + 18glox = (30glo + 15glox) Solving -24glo + 18glox = 30glo + 15glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. -24glo + -30glo + 18glox = 30glo + -30glo + 15glox Combine like terms: -24glo + -30glo = -54glo -54glo + 18glox = 30glo + -30glo + 15glox Combine like terms: 30glo + -30glo = 0 -54glo + 18glox = 0 + 15glox -54glo + 18glox = 15glox Add '-15glox' to each side of the equation. -54glo + 18glox + -15glox = 15glox + -15glox Combine like terms: 18glox + -15glox = 3glox -54glo + 3glox = 15glox + -15glox Combine like terms: 15glox + -15glox = 0 -54glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-18 + x) = 0 Ignore the factor 3.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 '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Add '-1x' to each side of the equation. x + -1x = 18 + -1x Combine like terms: x + -1x = 0 0 = 18 + -1x Simplifying 0 = 18 + -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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