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