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Simplifying ln(6x + -1) = ln(1) + -1ln(x + -1) Reorder the terms: ln(-1 + 6x) = ln(1) + -1ln(x + -1) (-1 * ln + 6x * ln) = ln(1) + -1ln(x + -1) (-1ln + 6lnx) = ln(1) + -1ln(x + -1) Reorder the terms for easier multiplication: -1ln + 6lnx = 1ln + -1ln(x + -1) Reorder the terms: -1ln + 6lnx = 1ln + -1ln(-1 + x) -1ln + 6lnx = 1ln + (-1 * -1ln + x * -1ln) -1ln + 6lnx = 1ln + (1ln + -1lnx) Combine like terms: 1ln + 1ln = 2ln -1ln + 6lnx = 2ln + -1lnx Solving -1ln + 6lnx = 2ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -1ln + -2ln + 6lnx = 2ln + -2ln + -1lnx Combine like terms: -1ln + -2ln = -3ln -3ln + 6lnx = 2ln + -2ln + -1lnx Combine like terms: 2ln + -2ln = 0 -3ln + 6lnx = 0 + -1lnx -3ln + 6lnx = -1lnx Add 'lnx' to each side of the equation. -3ln + 6lnx + lnx = -1lnx + lnx Combine like terms: 6lnx + lnx = 7lnx -3ln + 7lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -3ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 7x) = 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 + 7x)' equal to zero and attempt to solve: Simplifying -3 + 7x = 0 Solving -3 + 7x = 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 + 7x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7x = 0 + 3 7x = 0 + 3 Combine like terms: 0 + 3 = 3 7x = 3 Add '-7x' to each side of the equation. 7x + -7x = 3 + -7x Combine like terms: 7x + -7x = 0 0 = 3 + -7x Simplifying 0 = 3 + -7x 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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