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Simplifying ln(4x2 + -3x) = ln(16x + -12) + -1lnx Reorder the terms: ln(-3x + 4x2) = ln(16x + -12) + -1lnx (-3x * ln + 4x2 * ln) = ln(16x + -12) + -1lnx (-3lnx + 4lnx2) = ln(16x + -12) + -1lnx Reorder the terms: -3lnx + 4lnx2 = ln(-12 + 16x) + -1lnx -3lnx + 4lnx2 = (-12 * ln + 16x * ln) + -1lnx -3lnx + 4lnx2 = (-12ln + 16lnx) + -1lnx Combine like terms: 16lnx + -1lnx = 15lnx -3lnx + 4lnx2 = -12ln + 15lnx Solving -3lnx + 4lnx2 = -12ln + 15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. -3lnx + 12ln + 4lnx2 = -12ln + 12ln + 15lnx Reorder the terms: 12ln + -3lnx + 4lnx2 = -12ln + 12ln + 15lnx Combine like terms: -12ln + 12ln = 0 12ln + -3lnx + 4lnx2 = 0 + 15lnx 12ln + -3lnx + 4lnx2 = 15lnx Add '-15lnx' to each side of the equation. 12ln + -3lnx + -15lnx + 4lnx2 = 15lnx + -15lnx Combine like terms: -3lnx + -15lnx = -18lnx 12ln + -18lnx + 4lnx2 = 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 12ln + -18lnx + 4lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(6 + -9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + -9x + 2x2 = 0 Solving 6 + -9x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -9x + -6 + 2x2 = 0 + -6 Reorder the terms: 6 + -6 + -9x + 2x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9x + 2x2 = 0 + -6 -9x + 2x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9x + 2x2 = -6 Add '9x' to each side of the equation. -9x + 9x + 2x2 = -6 + 9x Combine like terms: -9x + 9x = 0 0 + 2x2 = -6 + 9x 2x2 = -6 + 9x Add '-2x2' to each side of the equation. 2x2 + -2x2 = -6 + 9x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = -6 + 9x + -2x2 Simplifying 0 = -6 + 9x + -2x2 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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