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Simplifying ln(x + -7) + -2ln(x + -1) = -2ln(5) Reorder the terms: ln(-7 + x) + -2ln(x + -1) = -2ln(5) (-7 * ln + x * ln) + -2ln(x + -1) = -2ln(5) (-7ln + lnx) + -2ln(x + -1) = -2ln(5) Reorder the terms: -7ln + lnx + -2ln(-1 + x) = -2ln(5) -7ln + lnx + (-1 * -2ln + x * -2ln) = -2ln(5) -7ln + lnx + (2ln + -2lnx) = -2ln(5) Reorder the terms: -7ln + 2ln + lnx + -2lnx = -2ln(5) Combine like terms: -7ln + 2ln = -5ln -5ln + lnx + -2lnx = -2ln(5) Combine like terms: lnx + -2lnx = -1lnx -5ln + -1lnx = -2ln(5) Reorder the terms for easier multiplication: -5ln + -1lnx = -2 * 5ln Multiply -2 * 5 -5ln + -1lnx = -10ln Solving -5ln + -1lnx = -10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. -5ln + 10ln + -1lnx = -10ln + 10ln Combine like terms: -5ln + 10ln = 5ln 5ln + -1lnx = -10ln + 10ln Combine like terms: -10ln + 10ln = 0 5ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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