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Simplifying ln(6x) + -1ln(x + -1) = ln(4) Remove parenthesis around (6x) ln * 6x + -1ln(x + -1) = ln(4) Reorder the terms for easier multiplication: 6ln * x + -1ln(x + -1) = ln(4) Multiply ln * x 6lnx + -1ln(x + -1) = ln(4) Reorder the terms: 6lnx + -1ln(-1 + x) = ln(4) 6lnx + (-1 * -1ln + x * -1ln) = ln(4) 6lnx + (1ln + -1lnx) = ln(4) Reorder the terms: 1ln + 6lnx + -1lnx = ln(4) Combine like terms: 6lnx + -1lnx = 5lnx 1ln + 5lnx = ln(4) Reorder the terms for easier multiplication: 1ln + 5lnx = 4ln Solving 1ln + 5lnx = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 1ln + -4ln + 5lnx = 4ln + -4ln Combine like terms: 1ln + -4ln = -3ln -3ln + 5lnx = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -3ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying -3 + 5x = 0 Solving -3 + 5x = 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 + 5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5x = 0 + 3 5x = 0 + 3 Combine like terms: 0 + 3 = 3 5x = 3 Add '-5x' to each side of the equation. 5x + -5x = 3 + -5x Combine like terms: 5x + -5x = 0 0 = 3 + -5x Simplifying 0 = 3 + -5x 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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