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