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