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Simplifying 2ln(x + -5) = ln(12x) Reorder the terms: 2ln(-5 + x) = ln(12x) (-5 * 2ln + x * 2ln) = ln(12x) (-10ln + 2lnx) = ln(12x) Remove parenthesis around (12x) -10ln + 2lnx = ln * 12x Reorder the terms for easier multiplication: -10ln + 2lnx = 12ln * x Multiply ln * x -10ln + 2lnx = 12lnx Solving -10ln + 2lnx = 12lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12lnx' to each side of the equation. -10ln + 2lnx + -12lnx = 12lnx + -12lnx Combine like terms: 2lnx + -12lnx = -10lnx -10ln + -10lnx = 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 -10ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '-10ln'. -10ln(1 + x) = 0 Ignore the factor -10.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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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