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