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Simplifying ln(x + 3) + ln(x + 2) = ln(x + -7) Reorder the terms: ln(3 + x) + ln(x + 2) = ln(x + -7) (3 * ln + x * ln) + ln(x + 2) = ln(x + -7) (3ln + lnx) + ln(x + 2) = ln(x + -7) Reorder the terms: 3ln + lnx + ln(2 + x) = ln(x + -7) 3ln + lnx + (2 * ln + x * ln) = ln(x + -7) 3ln + lnx + (2ln + lnx) = ln(x + -7) Reorder the terms: 3ln + 2ln + lnx + lnx = ln(x + -7) Combine like terms: 3ln + 2ln = 5ln 5ln + lnx + lnx = ln(x + -7) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = ln(x + -7) Reorder the terms: 5ln + 2lnx = ln(-7 + x) 5ln + 2lnx = (-7 * ln + x * ln) 5ln + 2lnx = (-7ln + lnx) Solving 5ln + 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. 5ln + 7ln + 2lnx = -7ln + 7ln + lnx Combine like terms: 5ln + 7ln = 12ln 12ln + 2lnx = -7ln + 7ln + lnx Combine like terms: -7ln + 7ln = 0 12ln + 2lnx = 0 + lnx 12ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 12ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 12ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 12ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -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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