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Simplifying ln * x + ln(x + -7) = ln * 7x + -1ln(x + -1) Multiply ln * x lnx + ln(x + -7) = ln * 7x + -1ln(x + -1) Reorder the terms: lnx + ln(-7 + x) = ln * 7x + -1ln(x + -1) lnx + (-7 * ln + x * ln) = ln * 7x + -1ln(x + -1) lnx + (-7ln + lnx) = ln * 7x + -1ln(x + -1) Reorder the terms: -7ln + lnx + lnx = ln * 7x + -1ln(x + -1) Combine like terms: lnx + lnx = 2lnx -7ln + 2lnx = ln * 7x + -1ln(x + -1) Reorder the terms for easier multiplication: -7ln + 2lnx = 7ln * x + -1ln(x + -1) Multiply ln * x -7ln + 2lnx = 7lnx + -1ln(x + -1) Reorder the terms: -7ln + 2lnx = 7lnx + -1ln(-1 + x) -7ln + 2lnx = 7lnx + (-1 * -1ln + x * -1ln) -7ln + 2lnx = 7lnx + (1ln + -1lnx) Reorder the terms: -7ln + 2lnx = 1ln + 7lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx -7ln + 2lnx = 1ln + 6lnx Solving -7ln + 2lnx = 1ln + 6lnx 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. -7ln + -1ln + 2lnx = 1ln + -1ln + 6lnx Combine like terms: -7ln + -1ln = -8ln -8ln + 2lnx = 1ln + -1ln + 6lnx Combine like terms: 1ln + -1ln = 0 -8ln + 2lnx = 0 + 6lnx -8ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. -8ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx -8ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -8ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-4ln'. -4ln(2 + x) = 0 Ignore the factor -4.Subproblem 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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