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Simplifying ln(2x + 5) = 2ln * x + -1ln(2 + -1x) Reorder the terms: ln(5 + 2x) = 2ln * x + -1ln(2 + -1x) (5 * ln + 2x * ln) = 2ln * x + -1ln(2 + -1x) (5ln + 2lnx) = 2ln * x + -1ln(2 + -1x) Multiply ln * x 5ln + 2lnx = 2lnx + -1ln(2 + -1x) 5ln + 2lnx = 2lnx + (2 * -1ln + -1x * -1ln) 5ln + 2lnx = 2lnx + (-2ln + 1lnx) Reorder the terms: 5ln + 2lnx = -2ln + 2lnx + 1lnx Combine like terms: 2lnx + 1lnx = 3lnx 5ln + 2lnx = -2ln + 3lnx Solving 5ln + 2lnx = -2ln + 3lnx 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. 5ln + 2ln + 2lnx = -2ln + 2ln + 3lnx Combine like terms: 5ln + 2ln = 7ln 7ln + 2lnx = -2ln + 2ln + 3lnx Combine like terms: -2ln + 2ln = 0 7ln + 2lnx = 0 + 3lnx 7ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 7ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 7ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 7ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x 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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