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Simplifying logx + log(x + -16) = log(8x) Reorder the terms: glox + glo(-16 + x) = log(8x) glox + (-16 * glo + x * glo) = log(8x) glox + (-16glo + glox) = log(8x) Reorder the terms: -16glo + glox + glox = log(8x) Combine like terms: glox + glox = 2glox -16glo + 2glox = log(8x) Remove parenthesis around (8x) -16glo + 2glox = glo * 8x Reorder the terms for easier multiplication: -16glo + 2glox = 8glo * x Multiply glo * x -16glo + 2glox = 8glox Solving -16glo + 2glox = 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glox' to each side of the equation. -16glo + 2glox + -8glox = 8glox + -8glox Combine like terms: 2glox + -8glox = -6glox -16glo + -6glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 -16glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(8 + 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 '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Add '-3x' to each side of the equation. 3x + -3x = -8 + -3x Combine like terms: 3x + -3x = 0 0 = -8 + -3x Simplifying 0 = -8 + -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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