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Simplifying log(5x + 2) + log(3) = log(14x + 15) Reorder the terms: glo(2 + 5x) + log(3) = log(14x + 15) (2 * glo + 5x * glo) + log(3) = log(14x + 15) (2glo + 5glox) + log(3) = log(14x + 15) Reorder the terms for easier multiplication: 2glo + 5glox + 3glo = log(14x + 15) Reorder the terms: 2glo + 3glo + 5glox = log(14x + 15) Combine like terms: 2glo + 3glo = 5glo 5glo + 5glox = log(14x + 15) Reorder the terms: 5glo + 5glox = glo(15 + 14x) 5glo + 5glox = (15 * glo + 14x * glo) 5glo + 5glox = (15glo + 14glox) Solving 5glo + 5glox = 15glo + 14glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-15glo' to each side of the equation. 5glo + -15glo + 5glox = 15glo + -15glo + 14glox Combine like terms: 5glo + -15glo = -10glo -10glo + 5glox = 15glo + -15glo + 14glox Combine like terms: 15glo + -15glo = 0 -10glo + 5glox = 0 + 14glox -10glo + 5glox = 14glox Add '-14glox' to each side of the equation. -10glo + 5glox + -14glox = 14glox + -14glox Combine like terms: 5glox + -14glox = -9glox -10glo + -9glox = 14glox + -14glox Combine like terms: 14glox + -14glox = 0 -10glo + -9glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(10 + 9x) = 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 '(10 + 9x)' equal to zero and attempt to solve: Simplifying 10 + 9x = 0 Solving 10 + 9x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 9x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9x = 0 + -10 9x = 0 + -10 Combine like terms: 0 + -10 = -10 9x = -10 Add '-9x' to each side of the equation. 9x + -9x = -10 + -9x Combine like terms: 9x + -9x = 0 0 = -10 + -9x Simplifying 0 = -10 + -9x 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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