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