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Simplifying log[12](-5x + -9) = log[12](-3x + -1) Reorder the terms: glo * 12(-9 + -5x) = log[12](-3x + -1) Reorder the terms for easier multiplication: 12glo(-9 + -5x) = log[12](-3x + -1) (-9 * 12glo + -5x * 12glo) = log[12](-3x + -1) (-108glo + -60glox) = log[12](-3x + -1) Reorder the terms: -108glo + -60glox = glo * 12(-1 + -3x) Reorder the terms for easier multiplication: -108glo + -60glox = 12glo(-1 + -3x) -108glo + -60glox = (-1 * 12glo + -3x * 12glo) -108glo + -60glox = (-12glo + -36glox) Solving -108glo + -60glox = -12glo + -36glox 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. -108glo + 12glo + -60glox = -12glo + 12glo + -36glox Combine like terms: -108glo + 12glo = -96glo -96glo + -60glox = -12glo + 12glo + -36glox Combine like terms: -12glo + 12glo = 0 -96glo + -60glox = 0 + -36glox -96glo + -60glox = -36glox Add '36glox' to each side of the equation. -96glo + -60glox + 36glox = -36glox + 36glox Combine like terms: -60glox + 36glox = -24glox -96glo + -24glox = -36glox + 36glox Combine like terms: -36glox + 36glox = 0 -96glo + -24glox = 0 Factor out the Greatest Common Factor (GCF), '-24glo'. -24glo(4 + x) = 0 Ignore the factor -24.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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