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Simplifying log(x + 8) = log(3x) Reorder the terms: glo(8 + x) = log(3x) (8 * glo + x * glo) = log(3x) (8glo + glox) = log(3x) Remove parenthesis around (3x) 8glo + glox = glo * 3x Reorder the terms for easier multiplication: 8glo + glox = 3glo * x Multiply glo * x 8glo + glox = 3glox Solving 8glo + glox = 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glox' to each side of the equation. 8glo + glox + -3glox = 3glox + -3glox Combine like terms: glox + -3glox = -2glox 8glo + -2glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 8glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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