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Simplifying log(x + 10) + -1log(2x + -5) = log(x + -4) Reorder the terms: glo(10 + x) + -1log(2x + -5) = log(x + -4) (10 * glo + x * glo) + -1log(2x + -5) = log(x + -4) (10glo + glox) + -1log(2x + -5) = log(x + -4) Reorder the terms: 10glo + glox + -1glo(-5 + 2x) = log(x + -4) 10glo + glox + (-5 * -1glo + 2x * -1glo) = log(x + -4) 10glo + glox + (5glo + -2glox) = log(x + -4) Reorder the terms: 10glo + 5glo + glox + -2glox = log(x + -4) Combine like terms: 10glo + 5glo = 15glo 15glo + glox + -2glox = log(x + -4) Combine like terms: glox + -2glox = -1glox 15glo + -1glox = log(x + -4) Reorder the terms: 15glo + -1glox = glo(-4 + x) 15glo + -1glox = (-4 * glo + x * glo) 15glo + -1glox = (-4glo + glox) Solving 15glo + -1glox = -4glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4glo' to each side of the equation. 15glo + 4glo + -1glox = -4glo + 4glo + glox Combine like terms: 15glo + 4glo = 19glo 19glo + -1glox = -4glo + 4glo + glox Combine like terms: -4glo + 4glo = 0 19glo + -1glox = 0 + glox 19glo + -1glox = glox Add '-1glox' to each side of the equation. 19glo + -1glox + -1glox = glox + -1glox Combine like terms: -1glox + -1glox = -2glox 19glo + -2glox = glox + -1glox Combine like terms: glox + -1glox = 0 19glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(19 + -2x) = 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 '(19 + -2x)' equal to zero and attempt to solve: Simplifying 19 + -2x = 0 Solving 19 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -2x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -2x = 0 + -19 -2x = 0 + -19 Combine like terms: 0 + -19 = -19 -2x = -19 Add '2x' to each side of the equation. -2x + 2x = -19 + 2x Combine like terms: -2x + 2x = 0 0 = -19 + 2x Simplifying 0 = -19 + 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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