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Simplifying log(x) + log(x + -9) = log(8x) Multiply glo * x glox + log(x + -9) = log(8x) Reorder the terms: glox + glo(-9 + x) = log(8x) glox + (-9 * glo + x * glo) = log(8x) glox + (-9glo + glox) = log(8x) Reorder the terms: -9glo + glox + glox = log(8x) Combine like terms: glox + glox = 2glox -9glo + 2glox = log(8x) Remove parenthesis around (8x) -9glo + 2glox = glo * 8x Reorder the terms for easier multiplication: -9glo + 2glox = 8glo * x Multiply glo * x -9glo + 2glox = 8glox Solving -9glo + 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. -9glo + 2glox + -8glox = 8glox + -8glox Combine like terms: 2glox + -8glox = -6glox -9glo + -6glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 -9glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(3 + 2x) = 0 Ignore the factor -3.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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -2x 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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