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Simplifying lnX + ln(X + 7) = ln(18) Reorder the terms: lnX + ln(7 + X) = ln(18) lnX + (7 * ln + X * ln) = ln(18) lnX + (7ln + lnX) = ln(18) Reorder the terms: 7ln + lnX + lnX = ln(18) Combine like terms: lnX + lnX = 2lnX 7ln + 2lnX = ln(18) Reorder the terms for easier multiplication: 7ln + 2lnX = 18ln Solving 7ln + 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. 7ln + -18ln + 2lnX = 18ln + -18ln Combine like terms: 7ln + -18ln = -11ln -11ln + 2lnX = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -11ln + 2lnX = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 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 '(-11 + 2X)' equal to zero and attempt to solve: Simplifying -11 + 2X = 0 Solving -11 + 2X = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2X = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2X = 0 + 11 2X = 0 + 11 Combine like terms: 0 + 11 = 11 2X = 11 Add '-2X' to each side of the equation. 2X + -2X = 11 + -2X Combine like terms: 2X + -2X = 0 0 = 11 + -2X Simplifying 0 = 11 + -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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