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Simplifying log(5x + 1) = log(2x + 3) Reorder the terms: glo(1 + 5x) = log(2x + 3) (1 * glo + 5x * glo) = log(2x + 3) (1glo + 5glox) = log(2x + 3) Reorder the terms: 1glo + 5glox = glo(3 + 2x) 1glo + 5glox = (3 * glo + 2x * glo) 1glo + 5glox = (3glo + 2glox) Solving 1glo + 5glox = 3glo + 2glox 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 + 5glox = 3glo + -3glo + 2glox Combine like terms: 1glo + -3glo = -2glo -2glo + 5glox = 3glo + -3glo + 2glox Combine like terms: 3glo + -3glo = 0 -2glo + 5glox = 0 + 2glox -2glo + 5glox = 2glox Add '-2glox' to each side of the equation. -2glo + 5glox + -2glox = 2glox + -2glox Combine like terms: 5glox + -2glox = 3glox -2glo + 3glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -2glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-2 + 3x) = 0Subproblem 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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