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Simplifying 2log * x + log * 2 = log(5x + 3) Multiply glo * x 2glox + log * 2 = log(5x + 3) Reorder the terms for easier multiplication: 2glox + 2glo = log(5x + 3) Reorder the terms: 2glo + 2glox = log(5x + 3) Reorder the terms: 2glo + 2glox = glo(3 + 5x) 2glo + 2glox = (3 * glo + 5x * glo) 2glo + 2glox = (3glo + 5glox) Solving 2glo + 2glox = 3glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glo' to each side of the equation. 2glo + -3glo + 2glox = 3glo + -3glo + 5glox Combine like terms: 2glo + -3glo = -1glo -1glo + 2glox = 3glo + -3glo + 5glox Combine like terms: 3glo + -3glo = 0 -1glo + 2glox = 0 + 5glox -1glo + 2glox = 5glox Add '-5glox' to each side of the equation. -1glo + 2glox + -5glox = 5glox + -5glox Combine like terms: 2glox + -5glox = -3glox -1glo + -3glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -1glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(1 + 3x) = 0 Ignore the factor -1.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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -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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