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Simplifying ln(6x + -5) + ln(x + -1) = ln * 5 Reorder the terms: ln(-5 + 6x) + ln(x + -1) = ln * 5 (-5 * ln + 6x * ln) + ln(x + -1) = ln * 5 (-5ln + 6lnx) + ln(x + -1) = ln * 5 Reorder the terms: -5ln + 6lnx + ln(-1 + x) = ln * 5 -5ln + 6lnx + (-1 * ln + x * ln) = ln * 5 -5ln + 6lnx + (-1ln + lnx) = ln * 5 Reorder the terms: -5ln + -1ln + 6lnx + lnx = ln * 5 Combine like terms: -5ln + -1ln = -6ln -6ln + 6lnx + lnx = ln * 5 Combine like terms: 6lnx + lnx = 7lnx -6ln + 7lnx = ln * 5 Reorder the terms for easier multiplication: -6ln + 7lnx = 5ln Solving -6ln + 7lnx = 5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -6ln + -5ln + 7lnx = 5ln + -5ln Combine like terms: -6ln + -5ln = -11ln -11ln + 7lnx = 5ln + -5ln Combine like terms: 5ln + -5ln = 0 -11ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 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 '(-11 + 7x)' equal to zero and attempt to solve: Simplifying -11 + 7x = 0 Solving -11 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 7x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 7x = 0 + 11 7x = 0 + 11 Combine like terms: 0 + 11 = 11 7x = 11 Add '-7x' to each side of the equation. 7x + -7x = 11 + -7x Combine like terms: 7x + -7x = 0 0 = 11 + -7x Simplifying 0 = 11 + -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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