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Simplifying ln(x + -5) + ln(x + -5) = 3ln(4) Reorder the terms: ln(-5 + x) + ln(x + -5) = 3ln(4) (-5 * ln + x * ln) + ln(x + -5) = 3ln(4) (-5ln + lnx) + ln(x + -5) = 3ln(4) Reorder the terms: -5ln + lnx + ln(-5 + x) = 3ln(4) -5ln + lnx + (-5 * ln + x * ln) = 3ln(4) -5ln + lnx + (-5ln + lnx) = 3ln(4) Reorder the terms: -5ln + -5ln + lnx + lnx = 3ln(4) Combine like terms: -5ln + -5ln = -10ln -10ln + lnx + lnx = 3ln(4) Combine like terms: lnx + lnx = 2lnx -10ln + 2lnx = 3ln(4) Reorder the terms for easier multiplication: -10ln + 2lnx = 3 * 4ln Multiply 3 * 4 -10ln + 2lnx = 12ln Solving -10ln + 2lnx = 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -10ln + -12ln + 2lnx = 12ln + -12ln Combine like terms: -10ln + -12ln = -22ln -22ln + 2lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -22ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-11 + x) = 0 Ignore the factor 2.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 '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 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 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Add '-1x' to each side of the equation. x + -1x = 11 + -1x Combine like terms: x + -1x = 0 0 = 11 + -1x Simplifying 0 = 11 + -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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