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Simplifying ln(x + -3) = ln(7x + -23) + -1ln(x + 1) Reorder the terms: ln(-3 + x) = ln(7x + -23) + -1ln(x + 1) (-3 * ln + x * ln) = ln(7x + -23) + -1ln(x + 1) (-3ln + lnx) = ln(7x + -23) + -1ln(x + 1) Reorder the terms: -3ln + lnx = ln(-23 + 7x) + -1ln(x + 1) -3ln + lnx = (-23 * ln + 7x * ln) + -1ln(x + 1) -3ln + lnx = (-23ln + 7lnx) + -1ln(x + 1) Reorder the terms: -3ln + lnx = -23ln + 7lnx + -1ln(1 + x) -3ln + lnx = -23ln + 7lnx + (1 * -1ln + x * -1ln) -3ln + lnx = -23ln + 7lnx + (-1ln + -1lnx) Reorder the terms: -3ln + lnx = -23ln + -1ln + 7lnx + -1lnx Combine like terms: -23ln + -1ln = -24ln -3ln + lnx = -24ln + 7lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx -3ln + lnx = -24ln + 6lnx Solving -3ln + lnx = -24ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '24ln' to each side of the equation. -3ln + 24ln + lnx = -24ln + 24ln + 6lnx Combine like terms: -3ln + 24ln = 21ln 21ln + lnx = -24ln + 24ln + 6lnx Combine like terms: -24ln + 24ln = 0 21ln + lnx = 0 + 6lnx 21ln + lnx = 6lnx Add '-6lnx' to each side of the equation. 21ln + lnx + -6lnx = 6lnx + -6lnx Combine like terms: lnx + -6lnx = -5lnx 21ln + -5lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 21ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(21 + -5x) = 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 '(21 + -5x)' equal to zero and attempt to solve: Simplifying 21 + -5x = 0 Solving 21 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -5x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -5x = 0 + -21 -5x = 0 + -21 Combine like terms: 0 + -21 = -21 -5x = -21 Add '5x' to each side of the equation. -5x + 5x = -21 + 5x Combine like terms: -5x + 5x = 0 0 = -21 + 5x Simplifying 0 = -21 + 5x 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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