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