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