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Simplifying log(x) + log(x + -10) = log(14x) Multiply glo * x glox + log(x + -10) = log(14x) Reorder the terms: glox + glo(-10 + x) = log(14x) glox + (-10 * glo + x * glo) = log(14x) glox + (-10glo + glox) = log(14x) Reorder the terms: -10glo + glox + glox = log(14x) Combine like terms: glox + glox = 2glox -10glo + 2glox = log(14x) Remove parenthesis around (14x) -10glo + 2glox = glo * 14x Reorder the terms for easier multiplication: -10glo + 2glox = 14glo * x Multiply glo * x -10glo + 2glox = 14glox Solving -10glo + 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. -10glo + 2glox + -14glox = 14glox + -14glox Combine like terms: 2glox + -14glox = -12glox -10glo + -12glox = 14glox + -14glox Combine like terms: 14glox + -14glox = 0 -10glo + -12glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(5 + 6x) = 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 '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Add '-6x' to each side of the equation. 6x + -6x = -5 + -6x Combine like terms: 6x + -6x = 0 0 = -5 + -6x Simplifying 0 = -5 + -6x 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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