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Simplifying log(4 + -3x) = log(x + 2) (4 * glo + -3x * glo) = log(x + 2) (4glo + -3glox) = log(x + 2) Reorder the terms: 4glo + -3glox = glo(2 + x) 4glo + -3glox = (2 * glo + x * glo) 4glo + -3glox = (2glo + glox) Solving 4glo + -3glox = 2glo + glox 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 + -3glox = 2glo + -2glo + glox Combine like terms: 4glo + -2glo = 2glo 2glo + -3glox = 2glo + -2glo + glox Combine like terms: 2glo + -2glo = 0 2glo + -3glox = 0 + glox 2glo + -3glox = glox Add '-1glox' to each side of the equation. 2glo + -3glox + -1glox = glox + -1glox Combine like terms: -3glox + -1glox = -4glox 2glo + -4glox = glox + -1glox Combine like terms: glox + -1glox = 0 2glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(1 + -2x) = 0 Ignore the factor 2.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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 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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