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Simplifying log(3) * x + log(3)(x + 3) = log(3)(x + 8) Reorder the terms for easier multiplication: 3glo * x + log(3)(x + 3) = log(3)(x + 8) Multiply glo * x 3glox + log(3)(x + 3) = log(3)(x + 8) Reorder the terms: 3glox + glo * 3(3 + x) = log(3)(x + 8) Reorder the terms for easier multiplication: 3glox + 3glo(3 + x) = log(3)(x + 8) 3glox + (3 * 3glo + x * 3glo) = log(3)(x + 8) 3glox + (9glo + 3glox) = log(3)(x + 8) Reorder the terms: 9glo + 3glox + 3glox = log(3)(x + 8) Combine like terms: 3glox + 3glox = 6glox 9glo + 6glox = log(3)(x + 8) Reorder the terms: 9glo + 6glox = glo * 3(8 + x) Reorder the terms for easier multiplication: 9glo + 6glox = 3glo(8 + x) 9glo + 6glox = (8 * 3glo + x * 3glo) 9glo + 6glox = (24glo + 3glox) Solving 9glo + 6glox = 24glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-24glo' to each side of the equation. 9glo + -24glo + 6glox = 24glo + -24glo + 3glox Combine like terms: 9glo + -24glo = -15glo -15glo + 6glox = 24glo + -24glo + 3glox Combine like terms: 24glo + -24glo = 0 -15glo + 6glox = 0 + 3glox -15glo + 6glox = 3glox Add '-3glox' to each side of the equation. -15glo + 6glox + -3glox = 3glox + -3glox Combine like terms: 6glox + -3glox = 3glox -15glo + 3glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -15glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-5 + x) = 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x 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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