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Simplifying 7ln(x + 5) = ln(x + -1) + -1ln(x + 1) Reorder the terms: 7ln(5 + x) = ln(x + -1) + -1ln(x + 1) (5 * 7ln + x * 7ln) = ln(x + -1) + -1ln(x + 1) (35ln + 7lnx) = ln(x + -1) + -1ln(x + 1) Reorder the terms: 35ln + 7lnx = ln(-1 + x) + -1ln(x + 1) 35ln + 7lnx = (-1 * ln + x * ln) + -1ln(x + 1) 35ln + 7lnx = (-1ln + lnx) + -1ln(x + 1) Reorder the terms: 35ln + 7lnx = -1ln + lnx + -1ln(1 + x) 35ln + 7lnx = -1ln + lnx + (1 * -1ln + x * -1ln) 35ln + 7lnx = -1ln + lnx + (-1ln + -1lnx) Reorder the terms: 35ln + 7lnx = -1ln + -1ln + lnx + -1lnx Combine like terms: -1ln + -1ln = -2ln 35ln + 7lnx = -2ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 35ln + 7lnx = -2ln + 0 35ln + 7lnx = -2ln Solving 35ln + 7lnx = -2ln 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. 35ln + 2ln + 7lnx = -2ln + 2ln Combine like terms: 35ln + 2ln = 37ln 37ln + 7lnx = -2ln + 2ln Combine like terms: -2ln + 2ln = 0 37ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(37 + 7x) = 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 '(37 + 7x)' equal to zero and attempt to solve: Simplifying 37 + 7x = 0 Solving 37 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + 7x = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 7x = 0 + -37 7x = 0 + -37 Combine like terms: 0 + -37 = -37 7x = -37 Add '-7x' to each side of the equation. 7x + -7x = -37 + -7x Combine like terms: 7x + -7x = 0 0 = -37 + -7x Simplifying 0 = -37 + -7x 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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