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