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Simplifying lnx = ln6 + -1ln(x + 5) Reorder the terms: lnx = ln6 + -1ln(5 + x) lnx = ln6 + (5 * -1ln + x * -1ln) lnx = ln6 + (-5ln + -1lnx) Reorder the terms: lnx = -5ln + -1lnx + ln6 Solving lnx = -5ln + -1lnx + ln6 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. 5ln + lnx = -5ln + -1lnx + 5ln + ln6 Reorder the terms: 5ln + lnx = -5ln + 5ln + -1lnx + ln6 Combine like terms: -5ln + 5ln = 0 5ln + lnx = 0 + -1lnx + ln6 5ln + lnx = -1lnx + ln6 Add 'lnx' to each side of the equation. 5ln + lnx + lnx = -1lnx + lnx + ln6 Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = -1lnx + lnx + ln6 Combine like terms: -1lnx + lnx = 0 5ln + 2lnx = 0 + ln6 5ln + 2lnx = ln6 Add '-1ln6' to each side of the equation. 5ln + 2lnx + -1ln6 = ln6 + -1ln6 Combine like terms: ln6 + -1ln6 = 0 5ln + 2lnx + -1ln6 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + 2x + -1n5) = 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 '(5 + 2x + -1n5)' equal to zero and attempt to solve: Simplifying 5 + 2x + -1n5 = 0 Reorder the terms: 5 + -1n5 + 2x = 0 Solving 5 + -1n5 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -1n5 + -5 + 2x = 0 + -5 Reorder the terms: 5 + -5 + -1n5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n5 + 2x = 0 + -5 -1n5 + 2x = 0 + -5 Combine like terms: 0 + -5 = -5 -1n5 + 2x = -5 Add 'n5' to each side of the equation. -1n5 + n5 + 2x = -5 + n5 Combine like terms: -1n5 + n5 = 0 0 + 2x = -5 + n5 2x = -5 + n5 Add '-2x' to each side of the equation. 2x + -2x = -5 + n5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + n5 + -2x Simplifying 0 = -5 + n5 + -2x 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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