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Simplifying ln(5x + -2) = ln(x + 6) Reorder the terms: ln(-2 + 5x) = ln(x + 6) (-2 * ln + 5x * ln) = ln(x + 6) (-2ln + 5lnx) = ln(x + 6) Reorder the terms: -2ln + 5lnx = ln(6 + x) -2ln + 5lnx = (6 * ln + x * ln) -2ln + 5lnx = (6ln + lnx) Solving -2ln + 5lnx = 6ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -2ln + -6ln + 5lnx = 6ln + -6ln + lnx Combine like terms: -2ln + -6ln = -8ln -8ln + 5lnx = 6ln + -6ln + lnx Combine like terms: 6ln + -6ln = 0 -8ln + 5lnx = 0 + lnx -8ln + 5lnx = lnx Add '-1lnx' to each side of the equation. -8ln + 5lnx + -1lnx = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx -8ln + 4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 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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