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Simplifying ln(7x + -13) = ln(2x + -17) Reorder the terms: ln(-13 + 7x) = ln(2x + -17) (-13 * ln + 7x * ln) = ln(2x + -17) (-13ln + 7lnx) = ln(2x + -17) Reorder the terms: -13ln + 7lnx = ln(-17 + 2x) -13ln + 7lnx = (-17 * ln + 2x * ln) -13ln + 7lnx = (-17ln + 2lnx) Solving -13ln + 7lnx = -17ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '17ln' to each side of the equation. -13ln + 17ln + 7lnx = -17ln + 17ln + 2lnx Combine like terms: -13ln + 17ln = 4ln 4ln + 7lnx = -17ln + 17ln + 2lnx Combine like terms: -17ln + 17ln = 0 4ln + 7lnx = 0 + 2lnx 4ln + 7lnx = 2lnx Add '-2lnx' to each side of the equation. 4ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx 4ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 4ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + 5x) = 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 '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Add '-5x' to each side of the equation. 5x + -5x = -4 + -5x Combine like terms: 5x + -5x = 0 0 = -4 + -5x Simplifying 0 = -4 + -5x 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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