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Simplifying ln(4x + 4) = ln(3x + -1) Reorder the terms: ln(4 + 4x) = ln(3x + -1) (4 * ln + 4x * ln) = ln(3x + -1) (4ln + 4lnx) = ln(3x + -1) Reorder the terms: 4ln + 4lnx = ln(-1 + 3x) 4ln + 4lnx = (-1 * ln + 3x * ln) 4ln + 4lnx = (-1ln + 3lnx) Solving 4ln + 4lnx = -1ln + 3lnx 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. 4ln + ln + 4lnx = -1ln + ln + 3lnx Combine like terms: 4ln + ln = 5ln 5ln + 4lnx = -1ln + ln + 3lnx Combine like terms: -1ln + ln = 0 5ln + 4lnx = 0 + 3lnx 5ln + 4lnx = 3lnx Add '-3lnx' to each side of the equation. 5ln + 4lnx + -3lnx = 3lnx + -3lnx Combine like terms: 4lnx + -3lnx = 1lnx 5ln + 1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 5ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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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