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Simplifying log(x + 3) = log(2) + -1log(x + 2) Reorder the terms: glo(3 + x) = log(2) + -1log(x + 2) (3 * glo + x * glo) = log(2) + -1log(x + 2) (3glo + glox) = log(2) + -1log(x + 2) Reorder the terms for easier multiplication: 3glo + glox = 2glo + -1log(x + 2) Reorder the terms: 3glo + glox = 2glo + -1glo(2 + x) 3glo + glox = 2glo + (2 * -1glo + x * -1glo) 3glo + glox = 2glo + (-2glo + -1glox) Combine like terms: 2glo + -2glo = 0 3glo + glox = 0 + -1glox 3glo + glox = -1glox Solving 3glo + glox = -1glox 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. 3glo + glox + glox = -1glox + glox Combine like terms: glox + glox = 2glox 3glo + 2glox = -1glox + glox Combine like terms: -1glox + glox = 0 3glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(3 + 2x) = 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 '(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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