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Simplifying 2log(x + 2) + logx = log(13x + 6) Reorder the terms: 2glo(2 + x) + logx = log(13x + 6) (2 * 2glo + x * 2glo) + logx = log(13x + 6) (4glo + 2glox) + logx = log(13x + 6) Combine like terms: 2glox + glox = 3glox 4glo + 3glox = log(13x + 6) Reorder the terms: 4glo + 3glox = glo(6 + 13x) 4glo + 3glox = (6 * glo + 13x * glo) 4glo + 3glox = (6glo + 13glox) Solving 4glo + 3glox = 6glo + 13glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 4glo + -6glo + 3glox = 6glo + -6glo + 13glox Combine like terms: 4glo + -6glo = -2glo -2glo + 3glox = 6glo + -6glo + 13glox Combine like terms: 6glo + -6glo = 0 -2glo + 3glox = 0 + 13glox -2glo + 3glox = 13glox Add '-13glox' to each side of the equation. -2glo + 3glox + -13glox = 13glox + -13glox Combine like terms: 3glox + -13glox = -10glox -2glo + -10glox = 13glox + -13glox Combine like terms: 13glox + -13glox = 0 -2glo + -10glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(1 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Add '-5x' to each side of the equation. 5x + -5x = -1 + -5x Combine like terms: 5x + -5x = 0 0 = -1 + -5x Simplifying 0 = -1 + -5x 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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