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Simplifying log(4x + -1) + -1log(x + 2) = logx Reorder the terms: glo(-1 + 4x) + -1log(x + 2) = logx (-1 * glo + 4x * glo) + -1log(x + 2) = logx (-1glo + 4glox) + -1log(x + 2) = logx Reorder the terms: -1glo + 4glox + -1glo(2 + x) = logx -1glo + 4glox + (2 * -1glo + x * -1glo) = logx -1glo + 4glox + (-2glo + -1glox) = logx Reorder the terms: -1glo + -2glo + 4glox + -1glox = logx Combine like terms: -1glo + -2glo = -3glo -3glo + 4glox + -1glox = logx Combine like terms: 4glox + -1glox = 3glox -3glo + 3glox = logx Solving -3glo + 3glox = glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glox' to each side of the equation. -3glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox -3glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 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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