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Simplifying ln(x + 4) + ln(x + 1) = 21ln(x + 3) Reorder the terms: ln(4 + x) + ln(x + 1) = 21ln(x + 3) (4 * ln + x * ln) + ln(x + 1) = 21ln(x + 3) (4ln + lnx) + ln(x + 1) = 21ln(x + 3) Reorder the terms: 4ln + lnx + ln(1 + x) = 21ln(x + 3) 4ln + lnx + (1 * ln + x * ln) = 21ln(x + 3) 4ln + lnx + (1ln + lnx) = 21ln(x + 3) Reorder the terms: 4ln + 1ln + lnx + lnx = 21ln(x + 3) Combine like terms: 4ln + 1ln = 5ln 5ln + lnx + lnx = 21ln(x + 3) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = 21ln(x + 3) Reorder the terms: 5ln + 2lnx = 21ln(3 + x) 5ln + 2lnx = (3 * 21ln + x * 21ln) 5ln + 2lnx = (63ln + 21lnx) Solving 5ln + 2lnx = 63ln + 21lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-63ln' to each side of the equation. 5ln + -63ln + 2lnx = 63ln + -63ln + 21lnx Combine like terms: 5ln + -63ln = -58ln -58ln + 2lnx = 63ln + -63ln + 21lnx Combine like terms: 63ln + -63ln = 0 -58ln + 2lnx = 0 + 21lnx -58ln + 2lnx = 21lnx Add '-21lnx' to each side of the equation. -58ln + 2lnx + -21lnx = 21lnx + -21lnx Combine like terms: 2lnx + -21lnx = -19lnx -58ln + -19lnx = 21lnx + -21lnx Combine like terms: 21lnx + -21lnx = 0 -58ln + -19lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(58 + 19x) = 0 Ignore the factor -1.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 '(58 + 19x)' equal to zero and attempt to solve: Simplifying 58 + 19x = 0 Solving 58 + 19x = 0 Move all terms containing l to the left, all other terms to the right. Add '-58' to each side of the equation. 58 + -58 + 19x = 0 + -58 Combine like terms: 58 + -58 = 0 0 + 19x = 0 + -58 19x = 0 + -58 Combine like terms: 0 + -58 = -58 19x = -58 Add '-19x' to each side of the equation. 19x + -19x = -58 + -19x Combine like terms: 19x + -19x = 0 0 = -58 + -19x Simplifying 0 = -58 + -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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