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Simplifying log(x) + log(x + -6) = log(14x) Multiply glo * x glox + log(x + -6) = log(14x) Reorder the terms: glox + glo(-6 + x) = log(14x) glox + (-6 * glo + x * glo) = log(14x) glox + (-6glo + glox) = log(14x) Reorder the terms: -6glo + glox + glox = log(14x) Combine like terms: glox + glox = 2glox -6glo + 2glox = log(14x) Remove parenthesis around (14x) -6glo + 2glox = glo * 14x Reorder the terms for easier multiplication: -6glo + 2glox = 14glo * x Multiply glo * x -6glo + 2glox = 14glox Solving -6glo + 2glox = 14glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-14glox' to each side of the equation. -6glo + 2glox + -14glox = 14glox + -14glox Combine like terms: 2glox + -14glox = -12glox -6glo + -12glox = 14glox + -14glox Combine like terms: 14glox + -14glox = 0 -6glo + -12glox = 0 Factor out the Greatest Common Factor (GCF), '-6glo'. -6glo(1 + 2x) = 0 Ignore the factor -6.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 + 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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