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Simplifying log(3) * x + log(3)(x + -2) = log(3) * 8x Reorder the terms for easier multiplication: 3glo * x + log(3)(x + -2) = log(3) * 8x Multiply glo * x 3glox + log(3)(x + -2) = log(3) * 8x Reorder the terms: 3glox + glo * 3(-2 + x) = log(3) * 8x Reorder the terms for easier multiplication: 3glox + 3glo(-2 + x) = log(3) * 8x 3glox + (-2 * 3glo + x * 3glo) = log(3) * 8x 3glox + (-6glo + 3glox) = log(3) * 8x Reorder the terms: -6glo + 3glox + 3glox = log(3) * 8x Combine like terms: 3glox + 3glox = 6glox -6glo + 6glox = log(3) * 8x Reorder the terms for easier multiplication: -6glo + 6glox = 3 * 8glo * x Multiply 3 * 8 -6glo + 6glox = 24glo * x Multiply glo * x -6glo + 6glox = 24glox Solving -6glo + 6glox = 24glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-24glox' to each side of the equation. -6glo + 6glox + -24glox = 24glox + -24glox Combine like terms: 6glox + -24glox = -18glox -6glo + -18glox = 24glox + -24glox Combine like terms: 24glox + -24glox = 0 -6glo + -18glox = 0 Factor out the Greatest Common Factor (GCF), '-6glo'. -6glo(1 + 3x) = 0 Ignore the factor -6.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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