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