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Simplifying log(x) + log(x + -12) = log(13x) Multiply glo * x glox + log(x + -12) = log(13x) Reorder the terms: glox + glo(-12 + x) = log(13x) glox + (-12 * glo + x * glo) = log(13x) glox + (-12glo + glox) = log(13x) Reorder the terms: -12glo + glox + glox = log(13x) Combine like terms: glox + glox = 2glox -12glo + 2glox = log(13x) Remove parenthesis around (13x) -12glo + 2glox = glo * 13x Reorder the terms for easier multiplication: -12glo + 2glox = 13glo * x Multiply glo * x -12glo + 2glox = 13glox Solving -12glo + 2glox = 13glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-13glox' to each side of the equation. -12glo + 2glox + -13glox = 13glox + -13glox Combine like terms: 2glox + -13glox = -11glox -12glo + -11glox = 13glox + -13glox Combine like terms: 13glox + -13glox = 0 -12glo + -11glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(12 + 11x) = 0 Ignore the factor -1.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 '(12 + 11x)' equal to zero and attempt to solve: Simplifying 12 + 11x = 0 Solving 12 + 11x = 0 Move all terms containing g to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 11x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11x = 0 + -12 11x = 0 + -12 Combine like terms: 0 + -12 = -12 11x = -12 Add '-11x' to each side of the equation. 11x + -11x = -12 + -11x Combine like terms: 11x + -11x = 0 0 = -12 + -11x Simplifying 0 = -12 + -11x 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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