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Simplifying log(x + -12) + log(x + -8) = log(8x + 96) Reorder the terms: glo(-12 + x) + log(x + -8) = log(8x + 96) (-12 * glo + x * glo) + log(x + -8) = log(8x + 96) (-12glo + glox) + log(x + -8) = log(8x + 96) Reorder the terms: -12glo + glox + glo(-8 + x) = log(8x + 96) -12glo + glox + (-8 * glo + x * glo) = log(8x + 96) -12glo + glox + (-8glo + glox) = log(8x + 96) Reorder the terms: -12glo + -8glo + glox + glox = log(8x + 96) Combine like terms: -12glo + -8glo = -20glo -20glo + glox + glox = log(8x + 96) Combine like terms: glox + glox = 2glox -20glo + 2glox = log(8x + 96) Reorder the terms: -20glo + 2glox = glo(96 + 8x) -20glo + 2glox = (96 * glo + 8x * glo) -20glo + 2glox = (96glo + 8glox) Solving -20glo + 2glox = 96glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-96glo' to each side of the equation. -20glo + -96glo + 2glox = 96glo + -96glo + 8glox Combine like terms: -20glo + -96glo = -116glo -116glo + 2glox = 96glo + -96glo + 8glox Combine like terms: 96glo + -96glo = 0 -116glo + 2glox = 0 + 8glox -116glo + 2glox = 8glox Add '-8glox' to each side of the equation. -116glo + 2glox + -8glox = 8glox + -8glox Combine like terms: 2glox + -8glox = -6glox -116glo + -6glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 -116glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(58 + 3x) = 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 '(58 + 3x)' equal to zero and attempt to solve: Simplifying 58 + 3x = 0 Solving 58 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-58' to each side of the equation. 58 + -58 + 3x = 0 + -58 Combine like terms: 58 + -58 = 0 0 + 3x = 0 + -58 3x = 0 + -58 Combine like terms: 0 + -58 = -58 3x = -58 Add '-3x' to each side of the equation. 3x + -3x = -58 + -3x Combine like terms: 3x + -3x = 0 0 = -58 + -3x Simplifying 0 = -58 + -3x 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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