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Simplifying 8ln(x) + -6ln(x) = ln(4x + 12) Multiply ln * x 8lnx + -6ln(x) = ln(4x + 12) Multiply ln * x 8lnx + -6lnx = ln(4x + 12) Combine like terms: 8lnx + -6lnx = 2lnx 2lnx = ln(4x + 12) Reorder the terms: 2lnx = ln(12 + 4x) 2lnx = (12 * ln + 4x * ln) 2lnx = (12ln + 4lnx) Solving 2lnx = 12ln + 4lnx 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. -12ln + 2lnx = 12ln + -12ln + 4lnx Combine like terms: 12ln + -12ln = 0 -12ln + 2lnx = 0 + 4lnx -12ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. -12ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx -12ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -12ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(6 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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