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Simplifying 2log(x + 5) = log(x + 7) Reorder the terms: 2glo(5 + x) = log(x + 7) (5 * 2glo + x * 2glo) = log(x + 7) (10glo + 2glox) = log(x + 7) Reorder the terms: 10glo + 2glox = glo(7 + x) 10glo + 2glox = (7 * glo + x * glo) 10glo + 2glox = (7glo + glox) Solving 10glo + 2glox = 7glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. 10glo + -7glo + 2glox = 7glo + -7glo + glox Combine like terms: 10glo + -7glo = 3glo 3glo + 2glox = 7glo + -7glo + glox Combine like terms: 7glo + -7glo = 0 3glo + 2glox = 0 + glox 3glo + 2glox = glox Add '-1glox' to each side of the equation. 3glo + 2glox + -1glox = glox + -1glox Combine like terms: 2glox + -1glox = 1glox 3glo + 1glox = glox + -1glox Combine like terms: glox + -1glox = 0 3glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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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