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Simplifying 2log(x + 1) + log(3x + 5) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) Reorder the terms: 2glo(1 + x) + log(3x + 5) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) (1 * 2glo + x * 2glo) + log(3x + 5) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) (2glo + 2glox) + log(3x + 5) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) Reorder the terms: 2glo + 2glox + glo(5 + 3x) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) 2glo + 2glox + (5 * glo + 3x * glo) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) 2glo + 2glox + (5glo + 3glox) + log(2) = log(6x + 1) + log(x + -2) + log(x + -2) Reorder the terms for easier multiplication: 2glo + 2glox + 5glo + 3glox + 2glo = log(6x + 1) + log(x + -2) + log(x + -2) Reorder the terms: 2glo + 5glo + 2glo + 2glox + 3glox = log(6x + 1) + log(x + -2) + log(x + -2) Combine like terms: 2glo + 5glo = 7glo 7glo + 2glo + 2glox + 3glox = log(6x + 1) + log(x + -2) + log(x + -2) Combine like terms: 7glo + 2glo = 9glo 9glo + 2glox + 3glox = log(6x + 1) + log(x + -2) + log(x + -2) Combine like terms: 2glox + 3glox = 5glox 9glo + 5glox = log(6x + 1) + log(x + -2) + log(x + -2) Reorder the terms: 9glo + 5glox = glo(1 + 6x) + log(x + -2) + log(x + -2) 9glo + 5glox = (1 * glo + 6x * glo) + log(x + -2) + log(x + -2) 9glo + 5glox = (1glo + 6glox) + log(x + -2) + log(x + -2) Reorder the terms: 9glo + 5glox = 1glo + 6glox + glo(-2 + x) + log(x + -2) 9glo + 5glox = 1glo + 6glox + (-2 * glo + x * glo) + log(x + -2) 9glo + 5glox = 1glo + 6glox + (-2glo + glox) + log(x + -2) Reorder the terms: 9glo + 5glox = 1glo + 6glox + -2glo + glox + glo(-2 + x) 9glo + 5glox = 1glo + 6glox + -2glo + glox + (-2 * glo + x * glo) 9glo + 5glox = 1glo + 6glox + -2glo + glox + (-2glo + glox) Reorder the terms: 9glo + 5glox = 1glo + -2glo + -2glo + 6glox + glox + glox Combine like terms: 1glo + -2glo = -1glo 9glo + 5glox = -1glo + -2glo + 6glox + glox + glox Combine like terms: -1glo + -2glo = -3glo 9glo + 5glox = -3glo + 6glox + glox + glox Combine like terms: 6glox + glox = 7glox 9glo + 5glox = -3glo + 7glox + glox Combine like terms: 7glox + glox = 8glox 9glo + 5glox = -3glo + 8glox Solving 9glo + 5glox = -3glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3glo' to each side of the equation. 9glo + 3glo + 5glox = -3glo + 3glo + 8glox Combine like terms: 9glo + 3glo = 12glo 12glo + 5glox = -3glo + 3glo + 8glox Combine like terms: -3glo + 3glo = 0 12glo + 5glox = 0 + 8glox 12glo + 5glox = 8glox Add '-8glox' to each side of the equation. 12glo + 5glox + -8glox = 8glox + -8glox Combine like terms: 5glox + -8glox = -3glox 12glo + -3glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 12glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(4 + -1x) = 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 '(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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