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Simplifying ln(5x + -6) + ln(x + -6) = ln(e) Reorder the terms: ln(-6 + 5x) + ln(x + -6) = ln(e) (-6 * ln + 5x * ln) + ln(x + -6) = ln(e) (-6ln + 5lnx) + ln(x + -6) = ln(e) Reorder the terms: -6ln + 5lnx + ln(-6 + x) = ln(e) -6ln + 5lnx + (-6 * ln + x * ln) = ln(e) -6ln + 5lnx + (-6ln + lnx) = ln(e) Reorder the terms: -6ln + -6ln + 5lnx + lnx = ln(e) Combine like terms: -6ln + -6ln = -12ln -12ln + 5lnx + lnx = ln(e) Combine like terms: 5lnx + lnx = 6lnx -12ln + 6lnx = ln(e) Multiply ln * e -12ln + 6lnx = eln Solving -12ln + 6lnx = eln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1eln' to each side of the equation. -12ln + -1eln + 6lnx = eln + -1eln Reorder the terms: -1eln + -12ln + 6lnx = eln + -1eln Combine like terms: eln + -1eln = 0 -1eln + -12ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1e + -12 + 6x) = 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 '(-1e + -12 + 6x)' equal to zero and attempt to solve: Simplifying -1e + -12 + 6x = 0 Reorder the terms: -12 + -1e + 6x = 0 Solving -12 + -1e + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -1e + 12 + 6x = 0 + 12 Reorder the terms: -12 + 12 + -1e + 6x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1e + 6x = 0 + 12 -1e + 6x = 0 + 12 Combine like terms: 0 + 12 = 12 -1e + 6x = 12 Add 'e' to each side of the equation. -1e + e + 6x = 12 + e Combine like terms: -1e + e = 0 0 + 6x = 12 + e 6x = 12 + e Add '-6x' to each side of the equation. 6x + -6x = 12 + e + -6x Combine like terms: 6x + -6x = 0 0 = 12 + e + -6x Simplifying 0 = 12 + e + -6x 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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