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Simplifying ln(6x + 2) + -1ln(x + 1) = ln(2h + -1) Reorder the terms: ln(2 + 6x) + -1ln(x + 1) = ln(2h + -1) (2 * ln + 6x * ln) + -1ln(x + 1) = ln(2h + -1) (2ln + 6lnx) + -1ln(x + 1) = ln(2h + -1) Reorder the terms: 2ln + 6lnx + -1ln(1 + x) = ln(2h + -1) 2ln + 6lnx + (1 * -1ln + x * -1ln) = ln(2h + -1) 2ln + 6lnx + (-1ln + -1lnx) = ln(2h + -1) Reorder the terms: 2ln + -1ln + 6lnx + -1lnx = ln(2h + -1) Combine like terms: 2ln + -1ln = 1ln 1ln + 6lnx + -1lnx = ln(2h + -1) Combine like terms: 6lnx + -1lnx = 5lnx 1ln + 5lnx = ln(2h + -1) Reorder the terms: 1ln + 5lnx = ln(-1 + 2h) 1ln + 5lnx = (-1 * ln + 2h * ln) Reorder the terms: 1ln + 5lnx = (2hln + -1ln) 1ln + 5lnx = (2hln + -1ln) Solving 1ln + 5lnx = 2hln + -1ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2hln' to each side of the equation. 1ln + -2hln + 5lnx = 2hln + -2hln + -1ln Reorder the terms: -2hln + 1ln + 5lnx = 2hln + -2hln + -1ln Combine like terms: 2hln + -2hln = 0 -2hln + 1ln + 5lnx = 0 + -1ln -2hln + 1ln + 5lnx = -1ln Add 'ln' to each side of the equation. -2hln + 1ln + ln + 5lnx = -1ln + ln Combine like terms: 1ln + ln = 2ln -2hln + 2ln + 5lnx = -1ln + ln Combine like terms: -1ln + ln = 0 -2hln + 2ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2h + 2 + 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 '(-2h + 2 + 5x)' equal to zero and attempt to solve: Simplifying -2h + 2 + 5x = 0 Reorder the terms: 2 + -2h + 5x = 0 Solving 2 + -2h + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2h + -2 + 5x = 0 + -2 Reorder the terms: 2 + -2 + -2h + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2h + 5x = 0 + -2 -2h + 5x = 0 + -2 Combine like terms: 0 + -2 = -2 -2h + 5x = -2 Add '2h' to each side of the equation. -2h + 2h + 5x = -2 + 2h Combine like terms: -2h + 2h = 0 0 + 5x = -2 + 2h 5x = -2 + 2h Add '-5x' to each side of the equation. 5x + -5x = -2 + 2h + -5x Combine like terms: 5x + -5x = 0 0 = -2 + 2h + -5x Simplifying 0 = -2 + 2h + -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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