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Simplifying log(2x + 5) = log(5x + 14) Reorder the terms: glo(5 + 2x) = log(5x + 14) (5 * glo + 2x * glo) = log(5x + 14) (5glo + 2glox) = log(5x + 14) Reorder the terms: 5glo + 2glox = glo(14 + 5x) 5glo + 2glox = (14 * glo + 5x * glo) 5glo + 2glox = (14glo + 5glox) Solving 5glo + 2glox = 14glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-14glo' to each side of the equation. 5glo + -14glo + 2glox = 14glo + -14glo + 5glox Combine like terms: 5glo + -14glo = -9glo -9glo + 2glox = 14glo + -14glo + 5glox Combine like terms: 14glo + -14glo = 0 -9glo + 2glox = 0 + 5glox -9glo + 2glox = 5glox Add '-5glox' to each side of the equation. -9glo + 2glox + -5glox = 5glox + -5glox Combine like terms: 2glox + -5glox = -3glox -9glo + -3glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -9glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(3 + x) = 0 Ignore the factor -3.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 '(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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