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