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Simplifying log(x + 14) + -1log(x) = log(x + 6) Reorder the terms: glo(14 + x) + -1log(x) = log(x + 6) (14 * glo + x * glo) + -1log(x) = log(x + 6) (14glo + glox) + -1log(x) = log(x + 6) Multiply glo * x 14glo + glox + -1glox = log(x + 6) Combine like terms: glox + -1glox = 0 14glo + 0 = log(x + 6) 14glo = log(x + 6) Reorder the terms: 14glo = glo(6 + x) 14glo = (6 * glo + x * glo) 14glo = (6glo + glox) Solving 14glo = 6glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 14glo + -6glo = 6glo + -6glo + glox Combine like terms: 14glo + -6glo = 8glo 8glo = 6glo + -6glo + glox Combine like terms: 6glo + -6glo = 0 8glo = 0 + glox 8glo = glox Add '-1glox' to each side of the equation. 8glo + -1glox = glox + -1glox Combine like terms: glox + -1glox = 0 8glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + x 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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