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Simplifying ln(x + 3) + ln(x + -4) + -1ln(x) = ln(3) Reorder the terms: ln(3 + x) + ln(x + -4) + -1ln(x) = ln(3) (3 * ln + x * ln) + ln(x + -4) + -1ln(x) = ln(3) (3ln + lnx) + ln(x + -4) + -1ln(x) = ln(3) Reorder the terms: 3ln + lnx + ln(-4 + x) + -1ln(x) = ln(3) 3ln + lnx + (-4 * ln + x * ln) + -1ln(x) = ln(3) 3ln + lnx + (-4ln + lnx) + -1ln(x) = ln(3) Multiply ln * x 3ln + lnx + -4ln + lnx + -1lnx = ln(3) Reorder the terms: 3ln + -4ln + lnx + lnx + -1lnx = ln(3) Combine like terms: 3ln + -4ln = -1ln -1ln + lnx + lnx + -1lnx = ln(3) Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx + -1lnx = ln(3) Combine like terms: 2lnx + -1lnx = 1lnx -1ln + 1lnx = ln(3) Reorder the terms for easier multiplication: -1ln + 1lnx = 3ln Solving -1ln + 1lnx = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -1ln + -3ln + 1lnx = 3ln + -3ln Combine like terms: -1ln + -3ln = -4ln -4ln + 1lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 -4ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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