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