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