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