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Simplifying ln(x + 5) + ln(x + -3) = 21lnx Reorder the terms: ln(5 + x) + ln(x + -3) = 21lnx (5 * ln + x * ln) + ln(x + -3) = 21lnx (5ln + lnx) + ln(x + -3) = 21lnx Reorder the terms: 5ln + lnx + ln(-3 + x) = 21lnx 5ln + lnx + (-3 * ln + x * ln) = 21lnx 5ln + lnx + (-3ln + lnx) = 21lnx Reorder the terms: 5ln + -3ln + lnx + lnx = 21lnx Combine like terms: 5ln + -3ln = 2ln 2ln + lnx + lnx = 21lnx Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = 21lnx Solving 2ln + 2lnx = 21lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21lnx' to each side of the equation. 2ln + 2lnx + -21lnx = 21lnx + -21lnx Combine like terms: 2lnx + -21lnx = -19lnx 2ln + -19lnx = 21lnx + -21lnx Combine like terms: 21lnx + -21lnx = 0 2ln + -19lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + -19x) = 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 '(2 + -19x)' equal to zero and attempt to solve: Simplifying 2 + -19x = 0 Solving 2 + -19x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -19x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -19x = 0 + -2 -19x = 0 + -2 Combine like terms: 0 + -2 = -2 -19x = -2 Add '19x' to each side of the equation. -19x + 19x = -2 + 19x Combine like terms: -19x + 19x = 0 0 = -2 + 19x Simplifying 0 = -2 + 19x 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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