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Simplifying ln(x + 3) + ln(x + -3) = ln(x + 11) Reorder the terms: ln(3 + x) + ln(x + -3) = ln(x + 11) (3 * ln + x * ln) + ln(x + -3) = ln(x + 11) (3ln + lnx) + ln(x + -3) = ln(x + 11) Reorder the terms: 3ln + lnx + ln(-3 + x) = ln(x + 11) 3ln + lnx + (-3 * ln + x * ln) = ln(x + 11) 3ln + lnx + (-3ln + lnx) = ln(x + 11) Reorder the terms: 3ln + -3ln + lnx + lnx = ln(x + 11) Combine like terms: 3ln + -3ln = 0 0 + lnx + lnx = ln(x + 11) lnx + lnx = ln(x + 11) Combine like terms: lnx + lnx = 2lnx 2lnx = ln(x + 11) Reorder the terms: 2lnx = ln(11 + x) 2lnx = (11 * ln + x * ln) 2lnx = (11ln + lnx) Solving 2lnx = 11ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. -11ln + 2lnx = 11ln + -11ln + lnx Combine like terms: 11ln + -11ln = 0 -11ln + 2lnx = 0 + lnx -11ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -11ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -11ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -11ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 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 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Add '-1x' to each side of the equation. x + -1x = 11 + -1x Combine like terms: x + -1x = 0 0 = 11 + -1x Simplifying 0 = 11 + -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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