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Simplifying log(2x + 1) + log(3x + 1) = 2log(2) Reorder the terms: glo(1 + 2x) + log(3x + 1) = 2log(2) (1 * glo + 2x * glo) + log(3x + 1) = 2log(2) (1glo + 2glox) + log(3x + 1) = 2log(2) Reorder the terms: 1glo + 2glox + glo(1 + 3x) = 2log(2) 1glo + 2glox + (1 * glo + 3x * glo) = 2log(2) 1glo + 2glox + (1glo + 3glox) = 2log(2) Reorder the terms: 1glo + 1glo + 2glox + 3glox = 2log(2) Combine like terms: 1glo + 1glo = 2glo 2glo + 2glox + 3glox = 2log(2) Combine like terms: 2glox + 3glox = 5glox 2glo + 5glox = 2log(2) Reorder the terms for easier multiplication: 2glo + 5glox = 2 * 2glo Multiply 2 * 2 2glo + 5glox = 4glo Solving 2glo + 5glox = 4glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 2glo + -4glo + 5glox = 4glo + -4glo Combine like terms: 2glo + -4glo = -2glo -2glo + 5glox = 4glo + -4glo Combine like terms: 4glo + -4glo = 0 -2glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-2 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying -2 + 5x = 0 Solving -2 + 5x = 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 + 5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x = 0 + 2 5x = 0 + 2 Combine like terms: 0 + 2 = 2 5x = 2 Add '-5x' to each side of the equation. 5x + -5x = 2 + -5x Combine like terms: 5x + -5x = 0 0 = 2 + -5x Simplifying 0 = 2 + -5x 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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