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Simplifying ln(x) + ln(x + 3) = ln(18) Multiply ln * x lnx + ln(x + 3) = ln(18) Reorder the terms: lnx + ln(3 + x) = ln(18) lnx + (3 * ln + x * ln) = ln(18) lnx + (3ln + lnx) = ln(18) Reorder the terms: 3ln + lnx + lnx = ln(18) Combine like terms: lnx + lnx = 2lnx 3ln + 2lnx = ln(18) Reorder the terms for easier multiplication: 3ln + 2lnx = 18ln Solving 3ln + 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. 3ln + -18ln + 2lnx = 18ln + -18ln Combine like terms: 3ln + -18ln = -15ln -15ln + 2lnx = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -15ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + 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 '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Add '-2x' to each side of the equation. 2x + -2x = 15 + -2x Combine like terms: 2x + -2x = 0 0 = 15 + -2x Simplifying 0 = 15 + -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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