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Simplifying log(x + -5) + -1log(x + 1) = log(2x + 1) Reorder the terms: glo(-5 + x) + -1log(x + 1) = log(2x + 1) (-5 * glo + x * glo) + -1log(x + 1) = log(2x + 1) (-5glo + glox) + -1log(x + 1) = log(2x + 1) Reorder the terms: -5glo + glox + -1glo(1 + x) = log(2x + 1) -5glo + glox + (1 * -1glo + x * -1glo) = log(2x + 1) -5glo + glox + (-1glo + -1glox) = log(2x + 1) Reorder the terms: -5glo + -1glo + glox + -1glox = log(2x + 1) Combine like terms: -5glo + -1glo = -6glo -6glo + glox + -1glox = log(2x + 1) Combine like terms: glox + -1glox = 0 -6glo + 0 = log(2x + 1) -6glo = log(2x + 1) Reorder the terms: -6glo = glo(1 + 2x) -6glo = (1 * glo + 2x * glo) -6glo = (1glo + 2glox) Solving -6glo = 1glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. -6glo + -1glo = 1glo + -1glo + 2glox Combine like terms: -6glo + -1glo = -7glo -7glo = 1glo + -1glo + 2glox Combine like terms: 1glo + -1glo = 0 -7glo = 0 + 2glox -7glo = 2glox Add '-2glox' to each side of the equation. -7glo + -2glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -7glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(7 + 2x) = 0 Ignore the factor -1.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 '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Add '-2x' to each side of the equation. 2x + -2x = -7 + -2x Combine like terms: 2x + -2x = 0 0 = -7 + -2x Simplifying 0 = -7 + -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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