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Simplifying log(4x + -6) = log(6x + -12) Reorder the terms: glo(-6 + 4x) = log(6x + -12) (-6 * glo + 4x * glo) = log(6x + -12) (-6glo + 4glox) = log(6x + -12) Reorder the terms: -6glo + 4glox = glo(-12 + 6x) -6glo + 4glox = (-12 * glo + 6x * glo) -6glo + 4glox = (-12glo + 6glox) Solving -6glo + 4glox = -12glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '12glo' to each side of the equation. -6glo + 12glo + 4glox = -12glo + 12glo + 6glox Combine like terms: -6glo + 12glo = 6glo 6glo + 4glox = -12glo + 12glo + 6glox Combine like terms: -12glo + 12glo = 0 6glo + 4glox = 0 + 6glox 6glo + 4glox = 6glox Add '-6glox' to each side of the equation. 6glo + 4glox + -6glox = 6glox + -6glox Combine like terms: 4glox + -6glox = -2glox 6glo + -2glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 6glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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