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Simplifying ln(x + 1) + ln(24) = ln(55) + ln(x) + -1ln(x + -1) Reorder the terms: ln(1 + x) + ln(24) = ln(55) + ln(x) + -1ln(x + -1) (1 * ln + x * ln) + ln(24) = ln(55) + ln(x) + -1ln(x + -1) (1ln + lnx) + ln(24) = ln(55) + ln(x) + -1ln(x + -1) Reorder the terms for easier multiplication: 1ln + lnx + 24ln = ln(55) + ln(x) + -1ln(x + -1) Reorder the terms: 1ln + 24ln + lnx = ln(55) + ln(x) + -1ln(x + -1) Combine like terms: 1ln + 24ln = 25ln 25ln + lnx = ln(55) + ln(x) + -1ln(x + -1) Reorder the terms for easier multiplication: 25ln + lnx = 55ln + ln(x) + -1ln(x + -1) Multiply ln * x 25ln + lnx = 55ln + lnx + -1ln(x + -1) Reorder the terms: 25ln + lnx = 55ln + lnx + -1ln(-1 + x) 25ln + lnx = 55ln + lnx + (-1 * -1ln + x * -1ln) 25ln + lnx = 55ln + lnx + (1ln + -1lnx) Reorder the terms: 25ln + lnx = 55ln + 1ln + lnx + -1lnx Combine like terms: 55ln + 1ln = 56ln 25ln + lnx = 56ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 25ln + lnx = 56ln + 0 25ln + lnx = 56ln Solving 25ln + lnx = 56ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-56ln' to each side of the equation. 25ln + -56ln + lnx = 56ln + -56ln Combine like terms: 25ln + -56ln = -31ln -31ln + lnx = 56ln + -56ln Combine like terms: 56ln + -56ln = 0 -31ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-31 + 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 '(-31 + x)' equal to zero and attempt to solve: Simplifying -31 + x = 0 Solving -31 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 0 + 31 Combine like terms: -31 + 31 = 0 0 + x = 0 + 31 x = 0 + 31 Combine like terms: 0 + 31 = 31 x = 31 Add '-1x' to each side of the equation. x + -1x = 31 + -1x Combine like terms: x + -1x = 0 0 = 31 + -1x Simplifying 0 = 31 + -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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