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Simplifying ln(5x + 2) + -1ln * x = ln * 6 Reorder the terms: ln(2 + 5x) + -1ln * x = ln * 6 (2 * ln + 5x * ln) + -1ln * x = ln * 6 (2ln + 5lnx) + -1ln * x = ln * 6 Multiply ln * x 2ln + 5lnx + -1lnx = ln * 6 Combine like terms: 5lnx + -1lnx = 4lnx 2ln + 4lnx = ln * 6 Reorder the terms for easier multiplication: 2ln + 4lnx = 6ln Solving 2ln + 4lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 2ln + -6ln + 4lnx = 6ln + -6ln Combine like terms: 2ln + -6ln = -4ln -4ln + 4lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -4ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-1 + x) = 0 Ignore the factor 4.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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