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Simplifying ln(x + -24) + ln(x + 100) = 3ln(5) Reorder the terms: ln(-24 + x) + ln(x + 100) = 3ln(5) (-24 * ln + x * ln) + ln(x + 100) = 3ln(5) (-24ln + lnx) + ln(x + 100) = 3ln(5) Reorder the terms: -24ln + lnx + ln(100 + x) = 3ln(5) -24ln + lnx + (100 * ln + x * ln) = 3ln(5) -24ln + lnx + (100ln + lnx) = 3ln(5) Reorder the terms: -24ln + 100ln + lnx + lnx = 3ln(5) Combine like terms: -24ln + 100ln = 76ln 76ln + lnx + lnx = 3ln(5) Combine like terms: lnx + lnx = 2lnx 76ln + 2lnx = 3ln(5) Reorder the terms for easier multiplication: 76ln + 2lnx = 3 * 5ln Multiply 3 * 5 76ln + 2lnx = 15ln Solving 76ln + 2lnx = 15ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 76ln + -15ln + 2lnx = 15ln + -15ln Combine like terms: 76ln + -15ln = 61ln 61ln + 2lnx = 15ln + -15ln Combine like terms: 15ln + -15ln = 0 61ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(61 + 2x) = 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 '(61 + 2x)' equal to zero and attempt to solve: Simplifying 61 + 2x = 0 Solving 61 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-61' to each side of the equation. 61 + -61 + 2x = 0 + -61 Combine like terms: 61 + -61 = 0 0 + 2x = 0 + -61 2x = 0 + -61 Combine like terms: 0 + -61 = -61 2x = -61 Add '-2x' to each side of the equation. 2x + -2x = -61 + -2x Combine like terms: 2x + -2x = 0 0 = -61 + -2x Simplifying 0 = -61 + -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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