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Simplifying logx(x + 2) = -1logx(x + 1) Reorder the terms: glox(2 + x) = -1logx(x + 1) (2 * glox + x * glox) = -1logx(x + 1) (2glox + glox2) = -1logx(x + 1) Reorder the terms: 2glox + glox2 = -1glox(1 + x) 2glox + glox2 = (1 * -1glox + x * -1glox) 2glox + glox2 = (-1glox + -1glox2) Solving 2glox + glox2 = -1glox + -1glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'glox' to each side of the equation. 2glox + glox + glox2 = -1glox + glox + -1glox2 Combine like terms: 2glox + glox = 3glox 3glox + glox2 = -1glox + glox + -1glox2 Combine like terms: -1glox + glox = 0 3glox + glox2 = 0 + -1glox2 3glox + glox2 = -1glox2 Add 'glox2' to each side of the equation. 3glox + glox2 + glox2 = -1glox2 + glox2 Combine like terms: glox2 + glox2 = 2glox2 3glox + 2glox2 = -1glox2 + glox2 Combine like terms: -1glox2 + glox2 = 0 3glox + 2glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glox'. glox(3 + 2x) = 0Subproblem 1
Set the factor 'glox' equal to zero and attempt to solve: Simplifying glox = 0 Solving glox = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glox = 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -2x 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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