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