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Simplifying log[3](4x + 19) + -1log[3](x + 3) = log[3](x + 1) Reorder the terms: glo * 3(19 + 4x) + -1log[3](x + 3) = log[3](x + 1) Reorder the terms for easier multiplication: 3glo(19 + 4x) + -1log[3](x + 3) = log[3](x + 1) (19 * 3glo + 4x * 3glo) + -1log[3](x + 3) = log[3](x + 1) (57glo + 12glox) + -1log[3](x + 3) = log[3](x + 1) Reorder the terms: 57glo + 12glox + -1glo * 3(3 + x) = log[3](x + 1) Reorder the terms for easier multiplication: 57glo + 12glox + -1 * 3glo(3 + x) = log[3](x + 1) Multiply -1 * 3 57glo + 12glox + -3glo(3 + x) = log[3](x + 1) 57glo + 12glox + (3 * -3glo + x * -3glo) = log[3](x + 1) 57glo + 12glox + (-9glo + -3glox) = log[3](x + 1) Reorder the terms: 57glo + -9glo + 12glox + -3glox = log[3](x + 1) Combine like terms: 57glo + -9glo = 48glo 48glo + 12glox + -3glox = log[3](x + 1) Combine like terms: 12glox + -3glox = 9glox 48glo + 9glox = log[3](x + 1) Reorder the terms: 48glo + 9glox = glo * 3(1 + x) Reorder the terms for easier multiplication: 48glo + 9glox = 3glo(1 + x) 48glo + 9glox = (1 * 3glo + x * 3glo) 48glo + 9glox = (3glo + 3glox) Solving 48glo + 9glox = 3glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glo' to each side of the equation. 48glo + -3glo + 9glox = 3glo + -3glo + 3glox Combine like terms: 48glo + -3glo = 45glo 45glo + 9glox = 3glo + -3glo + 3glox Combine like terms: 3glo + -3glo = 0 45glo + 9glox = 0 + 3glox 45glo + 9glox = 3glox Add '-3glox' to each side of the equation. 45glo + 9glox + -3glox = 3glox + -3glox Combine like terms: 9glox + -3glox = 6glox 45glo + 6glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 45glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(15 + 2x) = 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 '(15 + 2x)' equal to zero and attempt to solve: Simplifying 15 + 2x = 0 Solving 15 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2x = 0 + -15 2x = 0 + -15 Combine like terms: 0 + -15 = -15 2x = -15 Add '-2x' to each side of the equation. 2x + -2x = -15 + -2x Combine like terms: 2x + -2x = 0 0 = -15 + -2x Simplifying 0 = -15 + -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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