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Simplifying log(3x) = log(4) + log(x + 2) Remove parenthesis around (3x) glo * 3x = log(4) + log(x + 2) Reorder the terms for easier multiplication: 3glo * x = log(4) + log(x + 2) Multiply glo * x 3glox = log(4) + log(x + 2) Reorder the terms for easier multiplication: 3glox = 4glo + log(x + 2) Reorder the terms: 3glox = 4glo + glo(2 + x) 3glox = 4glo + (2 * glo + x * glo) 3glox = 4glo + (2glo + glox) Combine like terms: 4glo + 2glo = 6glo 3glox = 6glo + glox Solving 3glox = 6glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. -6glo + 3glox = 6glo + -6glo + glox Combine like terms: 6glo + -6glo = 0 -6glo + 3glox = 0 + glox -6glo + 3glox = glox Add '-1glox' to each side of the equation. -6glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox -6glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-3 + x) = 0 Ignore the factor 2.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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