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Simplifying Log[3](4x + 13) = log[3](9x + -2) Reorder the terms: goL * 3(13 + 4x) = log[3](9x + -2) Reorder the terms for easier multiplication: 3goL(13 + 4x) = log[3](9x + -2) (13 * 3goL + 4x * 3goL) = log[3](9x + -2) (39goL + 12goxL) = log[3](9x + -2) Reorder the terms: 39goL + 12goxL = glo * 3(-2 + 9x) Reorder the terms for easier multiplication: 39goL + 12goxL = 3glo(-2 + 9x) 39goL + 12goxL = (-2 * 3glo + 9x * 3glo) 39goL + 12goxL = (-6glo + 27glox) Solving 39goL + 12goxL = -6glo + 27glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6glo' to each side of the equation. 39goL + 6glo + 12goxL = -6glo + 6glo + 27glox Reorder the terms: 6glo + 39goL + 12goxL = -6glo + 6glo + 27glox Combine like terms: -6glo + 6glo = 0 6glo + 39goL + 12goxL = 0 + 27glox 6glo + 39goL + 12goxL = 27glox Add '-27glox' to each side of the equation. 6glo + 39goL + -27glox + 12goxL = 27glox + -27glox Reorder the terms: 6glo + -27glox + 39goL + 12goxL = 27glox + -27glox Combine like terms: 27glox + -27glox = 0 6glo + -27glox + 39goL + 12goxL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(2l + -9lx + 13L + 4xL) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(2l + -9lx + 13L + 4xL)' equal to zero and attempt to solve: Simplifying 2l + -9lx + 13L + 4xL = 0 Reorder the terms: 13L + 2l + -9lx + 4xL = 0 Solving 13L + 2l + -9lx + 4xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-13L' to each side of the equation. 13L + 2l + -9lx + -13L + 4xL = 0 + -13L Reorder the terms: 13L + -13L + 2l + -9lx + 4xL = 0 + -13L Combine like terms: 13L + -13L = 0 0 + 2l + -9lx + 4xL = 0 + -13L 2l + -9lx + 4xL = 0 + -13L Remove the zero: 2l + -9lx + 4xL = -13L Add '-2l' to each side of the equation. 2l + -9lx + -2l + 4xL = -13L + -2l Reorder the terms: 2l + -2l + -9lx + 4xL = -13L + -2l Combine like terms: 2l + -2l = 0 0 + -9lx + 4xL = -13L + -2l -9lx + 4xL = -13L + -2l Add '9lx' to each side of the equation. -9lx + 9lx + 4xL = -13L + -2l + 9lx Combine like terms: -9lx + 9lx = 0 0 + 4xL = -13L + -2l + 9lx 4xL = -13L + -2l + 9lx Add '-4xL' to each side of the equation. 4xL + -4xL = -13L + -2l + 9lx + -4xL Combine like terms: 4xL + -4xL = 0 0 = -13L + -2l + 9lx + -4xL Simplifying 0 = -13L + -2l + 9lx + -4xL 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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