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Simplifying log(3x) = log(2) + log(x + -1) Remove parenthesis around (3x) glo * 3x = log(2) + log(x + -1) Reorder the terms for easier multiplication: 3glo * x = log(2) + log(x + -1) Multiply glo * x 3glox = log(2) + log(x + -1) Reorder the terms for easier multiplication: 3glox = 2glo + log(x + -1) Reorder the terms: 3glox = 2glo + glo(-1 + x) 3glox = 2glo + (-1 * glo + x * glo) 3glox = 2glo + (-1glo + glox) Combine like terms: 2glo + -1glo = 1glo 3glox = 1glo + glox Solving 3glox = 1glo + glox 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. -1glo + 3glox = 1glo + -1glo + glox Combine like terms: 1glo + -1glo = 0 -1glo + 3glox = 0 + glox -1glo + 3glox = glox Add '-1glox' to each side of the equation. -1glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox -1glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 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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