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Simplifying ln(x + -3) + -1ln(11) = ln(13) Reorder the terms: ln(-3 + x) + -1ln(11) = ln(13) (-3 * ln + x * ln) + -1ln(11) = ln(13) (-3ln + lnx) + -1ln(11) = ln(13) Reorder the terms for easier multiplication: -3ln + lnx + -1 * 11ln = ln(13) Multiply -1 * 11 -3ln + lnx + -11ln = ln(13) Reorder the terms: -3ln + -11ln + lnx = ln(13) Combine like terms: -3ln + -11ln = -14ln -14ln + lnx = ln(13) Reorder the terms for easier multiplication: -14ln + lnx = 13ln Solving -14ln + lnx = 13ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-13ln' to each side of the equation. -14ln + -13ln + lnx = 13ln + -13ln Combine like terms: -14ln + -13ln = -27ln -27ln + lnx = 13ln + -13ln Combine like terms: 13ln + -13ln = 0 -27ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-27 + x) = 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 '(-27 + x)' equal to zero and attempt to solve: Simplifying -27 + x = 0 Solving -27 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + x = 0 + 27 x = 0 + 27 Combine like terms: 0 + 27 = 27 x = 27 Add '-1x' to each side of the equation. x + -1x = 27 + -1x Combine like terms: x + -1x = 0 0 = 27 + -1x Simplifying 0 = 27 + -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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