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Simplifying ln(5) + -1ln(x + -3) = ln(x + 1) Reorder the terms for easier multiplication: 5ln + -1ln(x + -3) = ln(x + 1) Reorder the terms: 5ln + -1ln(-3 + x) = ln(x + 1) 5ln + (-3 * -1ln + x * -1ln) = ln(x + 1) 5ln + (3ln + -1lnx) = ln(x + 1) Combine like terms: 5ln + 3ln = 8ln 8ln + -1lnx = ln(x + 1) Reorder the terms: 8ln + -1lnx = ln(1 + x) 8ln + -1lnx = (1 * ln + x * ln) 8ln + -1lnx = (1ln + lnx) Solving 8ln + -1lnx = 1ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 8ln + -1ln + -1lnx = 1ln + -1ln + lnx Combine like terms: 8ln + -1ln = 7ln 7ln + -1lnx = 1ln + -1ln + lnx Combine like terms: 1ln + -1ln = 0 7ln + -1lnx = 0 + lnx 7ln + -1lnx = lnx Add '-1lnx' to each side of the equation. 7ln + -1lnx + -1lnx = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx 7ln + -2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 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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