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