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Simplifying ln(x + 4) + ln(x + 3) = ln(6x + 18) Reorder the terms: ln(4 + x) + ln(x + 3) = ln(6x + 18) (4 * ln + x * ln) + ln(x + 3) = ln(6x + 18) (4ln + lnx) + ln(x + 3) = ln(6x + 18) Reorder the terms: 4ln + lnx + ln(3 + x) = ln(6x + 18) 4ln + lnx + (3 * ln + x * ln) = ln(6x + 18) 4ln + lnx + (3ln + lnx) = ln(6x + 18) Reorder the terms: 4ln + 3ln + lnx + lnx = ln(6x + 18) Combine like terms: 4ln + 3ln = 7ln 7ln + lnx + lnx = ln(6x + 18) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(6x + 18) Reorder the terms: 7ln + 2lnx = ln(18 + 6x) 7ln + 2lnx = (18 * ln + 6x * ln) 7ln + 2lnx = (18ln + 6lnx) Solving 7ln + 2lnx = 18ln + 6lnx 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 + 6lnx Combine like terms: 7ln + -18ln = -11ln -11ln + 2lnx = 18ln + -18ln + 6lnx Combine like terms: 18ln + -18ln = 0 -11ln + 2lnx = 0 + 6lnx -11ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. -11ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx -11ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -11ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(11 + 4x) = 0 Ignore the factor -1.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 '(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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