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Simplifying 2log(3)(x) = log(3)(5x + -4) Reorder the terms for easier multiplication: 2 * 3glo * x = log(3)(5x + -4) Multiply 2 * 3 6glo * x = log(3)(5x + -4) Multiply glo * x 6glox = log(3)(5x + -4) Reorder the terms: 6glox = glo * 3(-4 + 5x) Reorder the terms for easier multiplication: 6glox = 3glo(-4 + 5x) 6glox = (-4 * 3glo + 5x * 3glo) 6glox = (-12glo + 15glox) Solving 6glox = -12glo + 15glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '12glo' to each side of the equation. 12glo + 6glox = -12glo + 12glo + 15glox Combine like terms: -12glo + 12glo = 0 12glo + 6glox = 0 + 15glox 12glo + 6glox = 15glox Add '-15glox' to each side of the equation. 12glo + 6glox + -15glox = 15glox + -15glox Combine like terms: 6glox + -15glox = -9glox 12glo + -9glox = 15glox + -15glox Combine like terms: 15glox + -15glox = 0 12glo + -9glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Add '3x' to each side of the equation. -3x + 3x = -4 + 3x Combine like terms: -3x + 3x = 0 0 = -4 + 3x Simplifying 0 = -4 + 3x 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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