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Simplifying log(x + 1) + log(x) = 2log(3x + -5) Reorder the terms: glo(1 + x) + log(x) = 2log(3x + -5) (1 * glo + x * glo) + log(x) = 2log(3x + -5) (1glo + glox) + log(x) = 2log(3x + -5) Multiply glo * x 1glo + glox + glox = 2log(3x + -5) Combine like terms: glox + glox = 2glox 1glo + 2glox = 2log(3x + -5) Reorder the terms: 1glo + 2glox = 2glo(-5 + 3x) 1glo + 2glox = (-5 * 2glo + 3x * 2glo) 1glo + 2glox = (-10glo + 6glox) Solving 1glo + 2glox = -10glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '10glo' to each side of the equation. 1glo + 10glo + 2glox = -10glo + 10glo + 6glox Combine like terms: 1glo + 10glo = 11glo 11glo + 2glox = -10glo + 10glo + 6glox Combine like terms: -10glo + 10glo = 0 11glo + 2glox = 0 + 6glox 11glo + 2glox = 6glox Add '-6glox' to each side of the equation. 11glo + 2glox + -6glox = 6glox + -6glox Combine like terms: 2glox + -6glox = -4glox 11glo + -4glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 11glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(11 + -4x) = 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 '(11 + -4x)' equal to zero and attempt to solve: Simplifying 11 + -4x = 0 Solving 11 + -4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4x = 0 + -11 -4x = 0 + -11 Combine like terms: 0 + -11 = -11 -4x = -11 Add '4x' to each side of the equation. -4x + 4x = -11 + 4x Combine like terms: -4x + 4x = 0 0 = -11 + 4x Simplifying 0 = -11 + 4x 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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