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