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