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Simplifying ln(x + 2) = ln(12) + -1ln(x + 3) Reorder the terms: ln(2 + x) = ln(12) + -1ln(x + 3) (2 * ln + x * ln) = ln(12) + -1ln(x + 3) (2ln + lnx) = ln(12) + -1ln(x + 3) Reorder the terms for easier multiplication: 2ln + lnx = 12ln + -1ln(x + 3) Reorder the terms: 2ln + lnx = 12ln + -1ln(3 + x) 2ln + lnx = 12ln + (3 * -1ln + x * -1ln) 2ln + lnx = 12ln + (-3ln + -1lnx) Combine like terms: 12ln + -3ln = 9ln 2ln + lnx = 9ln + -1lnx Solving 2ln + lnx = 9ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 2ln + -9ln + lnx = 9ln + -9ln + -1lnx Combine like terms: 2ln + -9ln = -7ln -7ln + lnx = 9ln + -9ln + -1lnx Combine like terms: 9ln + -9ln = 0 -7ln + lnx = 0 + -1lnx -7ln + lnx = -1lnx Add 'lnx' to each side of the equation. -7ln + lnx + lnx = -1lnx + lnx Combine like terms: lnx + lnx = 2lnx -7ln + 2lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -7ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 2x) = 0Subproblem 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 '(-7 + 2x)' equal to zero and attempt to solve: Simplifying -7 + 2x = 0 Solving -7 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x = 0 + 7 2x = 0 + 7 Combine like terms: 0 + 7 = 7 2x = 7 Add '-2x' to each side of the equation. 2x + -2x = 7 + -2x Combine like terms: 2x + -2x = 0 0 = 7 + -2x Simplifying 0 = 7 + -2x 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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