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Simplifying ln(6x + 18) = ln(x + 4) + ln(x + 3) Reorder the terms: ln(18 + 6x) = ln(x + 4) + ln(x + 3) (18 * ln + 6x * ln) = ln(x + 4) + ln(x + 3) (18ln + 6lnx) = ln(x + 4) + ln(x + 3) Reorder the terms: 18ln + 6lnx = ln(4 + x) + ln(x + 3) 18ln + 6lnx = (4 * ln + x * ln) + ln(x + 3) 18ln + 6lnx = (4ln + lnx) + ln(x + 3) Reorder the terms: 18ln + 6lnx = 4ln + lnx + ln(3 + x) 18ln + 6lnx = 4ln + lnx + (3 * ln + x * ln) 18ln + 6lnx = 4ln + lnx + (3ln + lnx) Reorder the terms: 18ln + 6lnx = 4ln + 3ln + lnx + lnx Combine like terms: 4ln + 3ln = 7ln 18ln + 6lnx = 7ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 18ln + 6lnx = 7ln + 2lnx Solving 18ln + 6lnx = 7ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 18ln + -7ln + 6lnx = 7ln + -7ln + 2lnx Combine like terms: 18ln + -7ln = 11ln 11ln + 6lnx = 7ln + -7ln + 2lnx Combine like terms: 7ln + -7ln = 0 11ln + 6lnx = 0 + 2lnx 11ln + 6lnx = 2lnx Add '-2lnx' to each side of the equation. 11ln + 6lnx + -2lnx = 2lnx + -2lnx Combine like terms: 6lnx + -2lnx = 4lnx 11ln + 4lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 11ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + 4x) = 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 + 4x)' equal to zero and attempt to solve: Simplifying 11 + 4x = 0 Solving 11 + 4x = 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 + 4x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 4x = 0 + -11 4x = 0 + -11 Combine like terms: 0 + -11 = -11 4x = -11 Add '-4x' to each side of the equation. 4x + -4x = -11 + -4x Combine like terms: 4x + -4x = 0 0 = -11 + -4x Simplifying 0 = -11 + -4x 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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