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Simplifying log(4x + 3) + log(3) = log(11x + 12) Reorder the terms: glo(3 + 4x) + log(3) = log(11x + 12) (3 * glo + 4x * glo) + log(3) = log(11x + 12) (3glo + 4glox) + log(3) = log(11x + 12) Reorder the terms for easier multiplication: 3glo + 4glox + 3glo = log(11x + 12) Reorder the terms: 3glo + 3glo + 4glox = log(11x + 12) Combine like terms: 3glo + 3glo = 6glo 6glo + 4glox = log(11x + 12) Reorder the terms: 6glo + 4glox = glo(12 + 11x) 6glo + 4glox = (12 * glo + 11x * glo) 6glo + 4glox = (12glo + 11glox) Solving 6glo + 4glox = 12glo + 11glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. 6glo + -12glo + 4glox = 12glo + -12glo + 11glox Combine like terms: 6glo + -12glo = -6glo -6glo + 4glox = 12glo + -12glo + 11glox Combine like terms: 12glo + -12glo = 0 -6glo + 4glox = 0 + 11glox -6glo + 4glox = 11glox Add '-11glox' to each side of the equation. -6glo + 4glox + -11glox = 11glox + -11glox Combine like terms: 4glox + -11glox = -7glox -6glo + -7glox = 11glox + -11glox Combine like terms: 11glox + -11glox = 0 -6glo + -7glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(6 + 7x) = 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 '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Add '-7x' to each side of the equation. 7x + -7x = -6 + -7x Combine like terms: 7x + -7x = 0 0 = -6 + -7x Simplifying 0 = -6 + -7x 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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