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Simplifying ln(4 + -1x) + ln(x + 3) = ln(2 + -2x) (4 * ln + -1x * ln) + ln(x + 3) = ln(2 + -2x) (4ln + -1lnx) + ln(x + 3) = ln(2 + -2x) Reorder the terms: 4ln + -1lnx + ln(3 + x) = ln(2 + -2x) 4ln + -1lnx + (3 * ln + x * ln) = ln(2 + -2x) 4ln + -1lnx + (3ln + lnx) = ln(2 + -2x) Reorder the terms: 4ln + 3ln + -1lnx + lnx = ln(2 + -2x) Combine like terms: 4ln + 3ln = 7ln 7ln + -1lnx + lnx = ln(2 + -2x) Combine like terms: -1lnx + lnx = 0 7ln + 0 = ln(2 + -2x) 7ln = ln(2 + -2x) 7ln = (2 * ln + -2x * ln) 7ln = (2ln + -2lnx) Solving 7ln = 2ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 7ln + -2ln = 2ln + -2ln + -2lnx Combine like terms: 7ln + -2ln = 5ln 5ln = 2ln + -2ln + -2lnx Combine like terms: 2ln + -2ln = 0 5ln = 0 + -2lnx 5ln = -2lnx Add '2lnx' to each side of the equation. 5ln + 2lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 5ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + 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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -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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