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Simplifying log(x) + log(x + -2) = log(8x) Multiply glo * x glox + log(x + -2) = log(8x) Reorder the terms: glox + glo(-2 + x) = log(8x) glox + (-2 * glo + x * glo) = log(8x) glox + (-2glo + glox) = log(8x) Reorder the terms: -2glo + glox + glox = log(8x) Combine like terms: glox + glox = 2glox -2glo + 2glox = log(8x) Remove parenthesis around (8x) -2glo + 2glox = glo * 8x Reorder the terms for easier multiplication: -2glo + 2glox = 8glo * x Multiply glo * x -2glo + 2glox = 8glox Solving -2glo + 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. -2glo + 2glox + -8glox = 8glox + -8glox Combine like terms: 2glox + -8glox = -6glox -2glo + -6glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 -2glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(1 + 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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -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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