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Simplifying ln(x + 3) + ln(x + -2) = ln(14) Reorder the terms: ln(3 + x) + ln(x + -2) = ln(14) (3 * ln + x * ln) + ln(x + -2) = ln(14) (3ln + lnx) + ln(x + -2) = ln(14) Reorder the terms: 3ln + lnx + ln(-2 + x) = ln(14) 3ln + lnx + (-2 * ln + x * ln) = ln(14) 3ln + lnx + (-2ln + lnx) = ln(14) Reorder the terms: 3ln + -2ln + lnx + lnx = ln(14) Combine like terms: 3ln + -2ln = 1ln 1ln + lnx + lnx = ln(14) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(14) Reorder the terms for easier multiplication: 1ln + 2lnx = 14ln Solving 1ln + 2lnx = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 1ln + -14ln + 2lnx = 14ln + -14ln Combine like terms: 1ln + -14ln = -13ln -13ln + 2lnx = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -13ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 2x) = 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 '(-13 + 2x)' equal to zero and attempt to solve: Simplifying -13 + 2x = 0 Solving -13 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x = 0 + 13 2x = 0 + 13 Combine like terms: 0 + 13 = 13 2x = 13 Add '-2x' to each side of the equation. 2x + -2x = 13 + -2x Combine like terms: 2x + -2x = 0 0 = 13 + -2x Simplifying 0 = 13 + -2x 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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