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Simplifying log(5x + 3) + log(3) = log(14x + 15) Reorder the terms: glo(3 + 5x) + log(3) = log(14x + 15) (3 * glo + 5x * glo) + log(3) = log(14x + 15) (3glo + 5glox) + log(3) = log(14x + 15) Reorder the terms for easier multiplication: 3glo + 5glox + 3glo = log(14x + 15) Reorder the terms: 3glo + 3glo + 5glox = log(14x + 15) Combine like terms: 3glo + 3glo = 6glo 6glo + 5glox = log(14x + 15) Reorder the terms: 6glo + 5glox = glo(15 + 14x) 6glo + 5glox = (15 * glo + 14x * glo) 6glo + 5glox = (15glo + 14glox) Solving 6glo + 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. 6glo + -15glo + 5glox = 15glo + -15glo + 14glox Combine like terms: 6glo + -15glo = -9glo -9glo + 5glox = 15glo + -15glo + 14glox Combine like terms: 15glo + -15glo = 0 -9glo + 5glox = 0 + 14glox -9glo + 5glox = 14glox Add '-14glox' to each side of the equation. -9glo + 5glox + -14glox = 14glox + -14glox Combine like terms: 5glox + -14glox = -9glox -9glo + -9glox = 14glox + -14glox Combine like terms: 14glox + -14glox = 0 -9glo + -9glox = 0 Factor out the Greatest Common Factor (GCF), '-9glo'. -9glo(1 + x) = 0 Ignore the factor -9.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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