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Simplifying log(10 + -4x) = log(12 + -3x) (10 * glo + -4x * glo) = log(12 + -3x) (10glo + -4glox) = log(12 + -3x) 10glo + -4glox = (12 * glo + -3x * glo) 10glo + -4glox = (12glo + -3glox) Solving 10glo + -4glox = 12glo + -3glox 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. 10glo + -12glo + -4glox = 12glo + -12glo + -3glox Combine like terms: 10glo + -12glo = -2glo -2glo + -4glox = 12glo + -12glo + -3glox Combine like terms: 12glo + -12glo = 0 -2glo + -4glox = 0 + -3glox -2glo + -4glox = -3glox Add '3glox' to each side of the equation. -2glo + -4glox + 3glox = -3glox + 3glox Combine like terms: -4glox + 3glox = -1glox -2glo + -1glox = -3glox + 3glox Combine like terms: -3glox + 3glox = 0 -2glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(2 + x) = 0 Ignore the factor -1.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 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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