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Simplifying log(x + 5) + log(x + -2) = log(4x + -4) Reorder the terms: glo(5 + x) + log(x + -2) = log(4x + -4) (5 * glo + x * glo) + log(x + -2) = log(4x + -4) (5glo + glox) + log(x + -2) = log(4x + -4) Reorder the terms: 5glo + glox + glo(-2 + x) = log(4x + -4) 5glo + glox + (-2 * glo + x * glo) = log(4x + -4) 5glo + glox + (-2glo + glox) = log(4x + -4) Reorder the terms: 5glo + -2glo + glox + glox = log(4x + -4) Combine like terms: 5glo + -2glo = 3glo 3glo + glox + glox = log(4x + -4) Combine like terms: glox + glox = 2glox 3glo + 2glox = log(4x + -4) Reorder the terms: 3glo + 2glox = glo(-4 + 4x) 3glo + 2glox = (-4 * glo + 4x * glo) 3glo + 2glox = (-4glo + 4glox) Solving 3glo + 2glox = -4glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4glo' to each side of the equation. 3glo + 4glo + 2glox = -4glo + 4glo + 4glox Combine like terms: 3glo + 4glo = 7glo 7glo + 2glox = -4glo + 4glo + 4glox Combine like terms: -4glo + 4glo = 0 7glo + 2glox = 0 + 4glox 7glo + 2glox = 4glox Add '-4glox' to each side of the equation. 7glo + 2glox + -4glox = 4glox + -4glox Combine like terms: 2glox + -4glox = -2glox 7glo + -2glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 7glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(7 + -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 '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Add '2x' to each side of the equation. -2x + 2x = -7 + 2x Combine like terms: -2x + 2x = 0 0 = -7 + 2x Simplifying 0 = -7 + 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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