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