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Simplifying ln(x + 1) + ln(x + 3) = ln(x + 7) Reorder the terms: ln(1 + x) + ln(x + 3) = ln(x + 7) (1 * ln + x * ln) + ln(x + 3) = ln(x + 7) (1ln + lnx) + ln(x + 3) = ln(x + 7) Reorder the terms: 1ln + lnx + ln(3 + x) = ln(x + 7) 1ln + lnx + (3 * ln + x * ln) = ln(x + 7) 1ln + lnx + (3ln + lnx) = ln(x + 7) Reorder the terms: 1ln + 3ln + lnx + lnx = ln(x + 7) Combine like terms: 1ln + 3ln = 4ln 4ln + lnx + lnx = ln(x + 7) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(x + 7) Reorder the terms: 4ln + 2lnx = ln(7 + x) 4ln + 2lnx = (7 * ln + x * ln) 4ln + 2lnx = (7ln + lnx) Solving 4ln + 2lnx = 7ln + lnx 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. 4ln + -7ln + 2lnx = 7ln + -7ln + lnx Combine like terms: 4ln + -7ln = -3ln -3ln + 2lnx = 7ln + -7ln + lnx Combine like terms: 7ln + -7ln = 0 -3ln + 2lnx = 0 + lnx -3ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -3ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -3ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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