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Simplifying ln(x + -1) + ln(x + 2) = ln(45) Reorder the terms: ln(-1 + x) + ln(x + 2) = ln(45) (-1 * ln + x * ln) + ln(x + 2) = ln(45) (-1ln + lnx) + ln(x + 2) = ln(45) Reorder the terms: -1ln + lnx + ln(2 + x) = ln(45) -1ln + lnx + (2 * ln + x * ln) = ln(45) -1ln + lnx + (2ln + lnx) = ln(45) Reorder the terms: -1ln + 2ln + lnx + lnx = ln(45) Combine like terms: -1ln + 2ln = 1ln 1ln + lnx + lnx = ln(45) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(45) Reorder the terms for easier multiplication: 1ln + 2lnx = 45ln Solving 1ln + 2lnx = 45ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-45ln' to each side of the equation. 1ln + -45ln + 2lnx = 45ln + -45ln Combine like terms: 1ln + -45ln = -44ln -44ln + 2lnx = 45ln + -45ln Combine like terms: 45ln + -45ln = 0 -44ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-22 + x) = 0 Ignore the factor 2.Subproblem 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 '(-22 + x)' equal to zero and attempt to solve: Simplifying -22 + x = 0 Solving -22 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 0 + 22 Combine like terms: -22 + 22 = 0 0 + x = 0 + 22 x = 0 + 22 Combine like terms: 0 + 22 = 22 x = 22 Add '-1x' to each side of the equation. x + -1x = 22 + -1x Combine like terms: x + -1x = 0 0 = 22 + -1x Simplifying 0 = 22 + -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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