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Simplifying log(4x) + -1log(12 + x) = log(2) Remove parenthesis around (4x) glo * 4x + -1log(12 + x) = log(2) Reorder the terms for easier multiplication: 4glo * x + -1log(12 + x) = log(2) Multiply glo * x 4glox + -1log(12 + x) = log(2) 4glox + (12 * -1glo + x * -1glo) = log(2) 4glox + (-12glo + -1glox) = log(2) Reorder the terms: -12glo + 4glox + -1glox = log(2) Combine like terms: 4glox + -1glox = 3glox -12glo + 3glox = log(2) Reorder the terms for easier multiplication: -12glo + 3glox = 2glo Solving -12glo + 3glox = 2glo 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. -12glo + -2glo + 3glox = 2glo + -2glo Combine like terms: -12glo + -2glo = -14glo -14glo + 3glox = 2glo + -2glo Combine like terms: 2glo + -2glo = 0 -14glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-14 + 3x) = 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 '(-14 + 3x)' equal to zero and attempt to solve: Simplifying -14 + 3x = 0 Solving -14 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 3x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 3x = 0 + 14 3x = 0 + 14 Combine like terms: 0 + 14 = 14 3x = 14 Add '-3x' to each side of the equation. 3x + -3x = 14 + -3x Combine like terms: 3x + -3x = 0 0 = 14 + -3x Simplifying 0 = 14 + -3x 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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