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Simplifying ln(x + 2) + ln(x + -3) = ln(x + 56) Reorder the terms: ln(2 + x) + ln(x + -3) = ln(x + 56) (2 * ln + x * ln) + ln(x + -3) = ln(x + 56) (2ln + lnx) + ln(x + -3) = ln(x + 56) Reorder the terms: 2ln + lnx + ln(-3 + x) = ln(x + 56) 2ln + lnx + (-3 * ln + x * ln) = ln(x + 56) 2ln + lnx + (-3ln + lnx) = ln(x + 56) Reorder the terms: 2ln + -3ln + lnx + lnx = ln(x + 56) Combine like terms: 2ln + -3ln = -1ln -1ln + lnx + lnx = ln(x + 56) Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx = ln(x + 56) Reorder the terms: -1ln + 2lnx = ln(56 + x) -1ln + 2lnx = (56 * ln + x * ln) -1ln + 2lnx = (56ln + lnx) Solving -1ln + 2lnx = 56ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-56ln' to each side of the equation. -1ln + -56ln + 2lnx = 56ln + -56ln + lnx Combine like terms: -1ln + -56ln = -57ln -57ln + 2lnx = 56ln + -56ln + lnx Combine like terms: 56ln + -56ln = 0 -57ln + 2lnx = 0 + lnx -57ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -57ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -57ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -57ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-57 + 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 '(-57 + x)' equal to zero and attempt to solve: Simplifying -57 + x = 0 Solving -57 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '57' to each side of the equation. -57 + 57 + x = 0 + 57 Combine like terms: -57 + 57 = 0 0 + x = 0 + 57 x = 0 + 57 Combine like terms: 0 + 57 = 57 x = 57 Add '-1x' to each side of the equation. x + -1x = 57 + -1x Combine like terms: x + -1x = 0 0 = 57 + -1x Simplifying 0 = 57 + -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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