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Simplifying ln(x + -8) + ln(x + 18) = 3ln(3) Reorder the terms: ln(-8 + x) + ln(x + 18) = 3ln(3) (-8 * ln + x * ln) + ln(x + 18) = 3ln(3) (-8ln + lnx) + ln(x + 18) = 3ln(3) Reorder the terms: -8ln + lnx + ln(18 + x) = 3ln(3) -8ln + lnx + (18 * ln + x * ln) = 3ln(3) -8ln + lnx + (18ln + lnx) = 3ln(3) Reorder the terms: -8ln + 18ln + lnx + lnx = 3ln(3) Combine like terms: -8ln + 18ln = 10ln 10ln + lnx + lnx = 3ln(3) Combine like terms: lnx + lnx = 2lnx 10ln + 2lnx = 3ln(3) Reorder the terms for easier multiplication: 10ln + 2lnx = 3 * 3ln Multiply 3 * 3 10ln + 2lnx = 9ln Solving 10ln + 2lnx = 9ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 10ln + -9ln + 2lnx = 9ln + -9ln Combine like terms: 10ln + -9ln = 1ln 1ln + 2lnx = 9ln + -9ln Combine like terms: 9ln + -9ln = 0 1ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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