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Simplifying Log(6x + 1) = log(3x) Reorder the terms: goL(1 + 6x) = log(3x) (1 * goL + 6x * goL) = log(3x) (1goL + 6goxL) = log(3x) Remove parenthesis around (3x) 1goL + 6goxL = glo * 3x Reorder the terms for easier multiplication: 1goL + 6goxL = 3glo * x Multiply glo * x 1goL + 6goxL = 3glox Solving 1goL + 6goxL = 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glox' to each side of the equation. 1goL + -3glox + 6goxL = 3glox + -3glox Reorder the terms: -3glox + 1goL + 6goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -3glox + 1goL + 6goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-3lx + L + 6xL) = 0Subproblem 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 '(-3lx + L + 6xL)' equal to zero and attempt to solve: Simplifying -3lx + L + 6xL = 0 Reorder the terms: L + -3lx + 6xL = 0 Solving L + -3lx + 6xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -3lx + -1L + 6xL = 0 + -1L Reorder the terms: L + -1L + -3lx + 6xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -3lx + 6xL = 0 + -1L -3lx + 6xL = 0 + -1L Remove the zero: -3lx + 6xL = -1L Add '3lx' to each side of the equation. -3lx + 3lx + 6xL = -1L + 3lx Combine like terms: -3lx + 3lx = 0 0 + 6xL = -1L + 3lx 6xL = -1L + 3lx Add '-6xL' to each side of the equation. 6xL + -6xL = -1L + 3lx + -6xL Combine like terms: 6xL + -6xL = 0 0 = -1L + 3lx + -6xL Simplifying 0 = -1L + 3lx + -6xL 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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