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