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Simplifying log(13)(-4x + -1) = log(13)(2x + 5) Reorder the terms: glo * 13(-1 + -4x) = log(13)(2x + 5) Reorder the terms for easier multiplication: 13glo(-1 + -4x) = log(13)(2x + 5) (-1 * 13glo + -4x * 13glo) = log(13)(2x + 5) (-13glo + -52glox) = log(13)(2x + 5) Reorder the terms: -13glo + -52glox = glo * 13(5 + 2x) Reorder the terms for easier multiplication: -13glo + -52glox = 13glo(5 + 2x) -13glo + -52glox = (5 * 13glo + 2x * 13glo) -13glo + -52glox = (65glo + 26glox) Solving -13glo + -52glox = 65glo + 26glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-65glo' to each side of the equation. -13glo + -65glo + -52glox = 65glo + -65glo + 26glox Combine like terms: -13glo + -65glo = -78glo -78glo + -52glox = 65glo + -65glo + 26glox Combine like terms: 65glo + -65glo = 0 -78glo + -52glox = 0 + 26glox -78glo + -52glox = 26glox Add '-26glox' to each side of the equation. -78glo + -52glox + -26glox = 26glox + -26glox Combine like terms: -52glox + -26glox = -78glox -78glo + -78glox = 26glox + -26glox Combine like terms: 26glox + -26glox = 0 -78glo + -78glox = 0 Factor out the Greatest Common Factor (GCF), '-78glo'. -78glo(1 + x) = 0 Ignore the factor -78.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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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