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Simplifying ln(8x + -4) + -1ln(5x + 2) = ln(x + -1) Reorder the terms: ln(-4 + 8x) + -1ln(5x + 2) = ln(x + -1) (-4 * ln + 8x * ln) + -1ln(5x + 2) = ln(x + -1) (-4ln + 8lnx) + -1ln(5x + 2) = ln(x + -1) Reorder the terms: -4ln + 8lnx + -1ln(2 + 5x) = ln(x + -1) -4ln + 8lnx + (2 * -1ln + 5x * -1ln) = ln(x + -1) -4ln + 8lnx + (-2ln + -5lnx) = ln(x + -1) Reorder the terms: -4ln + -2ln + 8lnx + -5lnx = ln(x + -1) Combine like terms: -4ln + -2ln = -6ln -6ln + 8lnx + -5lnx = ln(x + -1) Combine like terms: 8lnx + -5lnx = 3lnx -6ln + 3lnx = ln(x + -1) Reorder the terms: -6ln + 3lnx = ln(-1 + x) -6ln + 3lnx = (-1 * ln + x * ln) -6ln + 3lnx = (-1ln + lnx) Solving -6ln + 3lnx = -1ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. -6ln + ln + 3lnx = -1ln + ln + lnx Combine like terms: -6ln + ln = -5ln -5ln + 3lnx = -1ln + ln + lnx Combine like terms: -1ln + ln = 0 -5ln + 3lnx = 0 + lnx -5ln + 3lnx = lnx Add '-1lnx' to each side of the equation. -5ln + 3lnx + -1lnx = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx -5ln + 2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Add '-2x' to each side of the equation. 2x + -2x = 5 + -2x Combine like terms: 2x + -2x = 0 0 = 5 + -2x Simplifying 0 = 5 + -2x 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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