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Simplifying ln(x + 1) = ln(5x + 7) + -1lnx Reorder the terms: ln(1 + x) = ln(5x + 7) + -1lnx (1 * ln + x * ln) = ln(5x + 7) + -1lnx (1ln + lnx) = ln(5x + 7) + -1lnx Reorder the terms: 1ln + lnx = ln(7 + 5x) + -1lnx 1ln + lnx = (7 * ln + 5x * ln) + -1lnx 1ln + lnx = (7ln + 5lnx) + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 1ln + lnx = 7ln + 4lnx Solving 1ln + lnx = 7ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 1ln + -7ln + lnx = 7ln + -7ln + 4lnx Combine like terms: 1ln + -7ln = -6ln -6ln + lnx = 7ln + -7ln + 4lnx Combine like terms: 7ln + -7ln = 0 -6ln + lnx = 0 + 4lnx -6ln + lnx = 4lnx Add '-4lnx' to each side of the equation. -6ln + lnx + -4lnx = 4lnx + -4lnx Combine like terms: lnx + -4lnx = -3lnx -6ln + -3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -6ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(2 + x) = 0 Ignore the factor -3.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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