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Simplifying log(x + 4) = log(4x + -2) Reorder the terms: glo(4 + x) = log(4x + -2) (4 * glo + x * glo) = log(4x + -2) (4glo + glox) = log(4x + -2) Reorder the terms: 4glo + glox = glo(-2 + 4x) 4glo + glox = (-2 * glo + 4x * glo) 4glo + glox = (-2glo + 4glox) Solving 4glo + glox = -2glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. 4glo + 2glo + glox = -2glo + 2glo + 4glox Combine like terms: 4glo + 2glo = 6glo 6glo + glox = -2glo + 2glo + 4glox Combine like terms: -2glo + 2glo = 0 6glo + glox = 0 + 4glox 6glo + glox = 4glox Add '-4glox' to each side of the equation. 6glo + glox + -4glox = 4glox + -4glox Combine like terms: glox + -4glox = -3glox 6glo + -3glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 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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