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Simplifying ln(x + 1) + ln(x + 4) = ln(x + 25) Reorder the terms: ln(1 + x) + ln(x + 4) = ln(x + 25) (1 * ln + x * ln) + ln(x + 4) = ln(x + 25) (1ln + lnx) + ln(x + 4) = ln(x + 25) Reorder the terms: 1ln + lnx + ln(4 + x) = ln(x + 25) 1ln + lnx + (4 * ln + x * ln) = ln(x + 25) 1ln + lnx + (4ln + lnx) = ln(x + 25) Reorder the terms: 1ln + 4ln + lnx + lnx = ln(x + 25) Combine like terms: 1ln + 4ln = 5ln 5ln + lnx + lnx = ln(x + 25) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = ln(x + 25) Reorder the terms: 5ln + 2lnx = ln(25 + x) 5ln + 2lnx = (25 * ln + x * ln) 5ln + 2lnx = (25ln + lnx) Solving 5ln + 2lnx = 25ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-25ln' to each side of the equation. 5ln + -25ln + 2lnx = 25ln + -25ln + lnx Combine like terms: 5ln + -25ln = -20ln -20ln + 2lnx = 25ln + -25ln + lnx Combine like terms: 25ln + -25ln = 0 -20ln + 2lnx = 0 + lnx -20ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -20ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -20ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -20ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-20 + 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 '(-20 + x)' equal to zero and attempt to solve: Simplifying -20 + x = 0 Solving -20 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + x = 0 + 20 x = 0 + 20 Combine like terms: 0 + 20 = 20 x = 20 Add '-1x' to each side of the equation. x + -1x = 20 + -1x Combine like terms: x + -1x = 0 0 = 20 + -1x Simplifying 0 = 20 + -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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