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Simplifying ln(x + 9) + ln(2x + 9) = ln(180) Reorder the terms: ln(9 + x) + ln(2x + 9) = ln(180) (9 * ln + x * ln) + ln(2x + 9) = ln(180) (9ln + lnx) + ln(2x + 9) = ln(180) Reorder the terms: 9ln + lnx + ln(9 + 2x) = ln(180) 9ln + lnx + (9 * ln + 2x * ln) = ln(180) 9ln + lnx + (9ln + 2lnx) = ln(180) Reorder the terms: 9ln + 9ln + lnx + 2lnx = ln(180) Combine like terms: 9ln + 9ln = 18ln 18ln + lnx + 2lnx = ln(180) Combine like terms: lnx + 2lnx = 3lnx 18ln + 3lnx = ln(180) Reorder the terms for easier multiplication: 18ln + 3lnx = 180ln Solving 18ln + 3lnx = 180ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-180ln' to each side of the equation. 18ln + -180ln + 3lnx = 180ln + -180ln Combine like terms: 18ln + -180ln = -162ln -162ln + 3lnx = 180ln + -180ln Combine like terms: 180ln + -180ln = 0 -162ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-54 + x) = 0 Ignore the factor 3.Subproblem 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 '(-54 + x)' equal to zero and attempt to solve: Simplifying -54 + x = 0 Solving -54 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + x = 0 + 54 Combine like terms: -54 + 54 = 0 0 + x = 0 + 54 x = 0 + 54 Combine like terms: 0 + 54 = 54 x = 54 Add '-1x' to each side of the equation. x + -1x = 54 + -1x Combine like terms: x + -1x = 0 0 = 54 + -1x Simplifying 0 = 54 + -1x 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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