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Simplifying ln(x + 2) + ln(x + 3) = ln(18) Reorder the terms: ln(2 + x) + ln(x + 3) = ln(18) (2 * ln + x * ln) + ln(x + 3) = ln(18) (2ln + lnx) + ln(x + 3) = ln(18) Reorder the terms: 2ln + lnx + ln(3 + x) = ln(18) 2ln + lnx + (3 * ln + x * ln) = ln(18) 2ln + lnx + (3ln + lnx) = ln(18) Reorder the terms: 2ln + 3ln + lnx + lnx = ln(18) Combine like terms: 2ln + 3ln = 5ln 5ln + lnx + lnx = ln(18) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = ln(18) Reorder the terms for easier multiplication: 5ln + 2lnx = 18ln Solving 5ln + 2lnx = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 5ln + -18ln + 2lnx = 18ln + -18ln Combine like terms: 5ln + -18ln = -13ln -13ln + 2lnx = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -13ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 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 '(-13 + 2x)' equal to zero and attempt to solve: Simplifying -13 + 2x = 0 Solving -13 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x = 0 + 13 2x = 0 + 13 Combine like terms: 0 + 13 = 13 2x = 13 Add '-2x' to each side of the equation. 2x + -2x = 13 + -2x Combine like terms: 2x + -2x = 0 0 = 13 + -2x Simplifying 0 = 13 + -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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