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Simplifying ln(2x + -5) = ln(5) + -1ln(x + -1) Reorder the terms: ln(-5 + 2x) = ln(5) + -1ln(x + -1) (-5 * ln + 2x * ln) = ln(5) + -1ln(x + -1) (-5ln + 2lnx) = ln(5) + -1ln(x + -1) Reorder the terms for easier multiplication: -5ln + 2lnx = 5ln + -1ln(x + -1) Reorder the terms: -5ln + 2lnx = 5ln + -1ln(-1 + x) -5ln + 2lnx = 5ln + (-1 * -1ln + x * -1ln) -5ln + 2lnx = 5ln + (1ln + -1lnx) Combine like terms: 5ln + 1ln = 6ln -5ln + 2lnx = 6ln + -1lnx Solving -5ln + 2lnx = 6ln + -1lnx 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. -5ln + -6ln + 2lnx = 6ln + -6ln + -1lnx Combine like terms: -5ln + -6ln = -11ln -11ln + 2lnx = 6ln + -6ln + -1lnx Combine like terms: 6ln + -6ln = 0 -11ln + 2lnx = 0 + -1lnx -11ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -11ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -11ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -11ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 3x) = 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 '(-11 + 3x)' equal to zero and attempt to solve: Simplifying -11 + 3x = 0 Solving -11 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 3x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3x = 0 + 11 3x = 0 + 11 Combine like terms: 0 + 11 = 11 3x = 11 Add '-3x' to each side of the equation. 3x + -3x = 11 + -3x Combine like terms: 3x + -3x = 0 0 = 11 + -3x Simplifying 0 = 11 + -3x 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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