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Simplifying lnx + ln(x + -13) = ln(x + -48) Reorder the terms: lnx + ln(-13 + x) = ln(x + -48) lnx + (-13 * ln + x * ln) = ln(x + -48) lnx + (-13ln + lnx) = ln(x + -48) Reorder the terms: -13ln + lnx + lnx = ln(x + -48) Combine like terms: lnx + lnx = 2lnx -13ln + 2lnx = ln(x + -48) Reorder the terms: -13ln + 2lnx = ln(-48 + x) -13ln + 2lnx = (-48 * ln + x * ln) -13ln + 2lnx = (-48ln + lnx) Solving -13ln + 2lnx = -48ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '48ln' to each side of the equation. -13ln + 48ln + 2lnx = -48ln + 48ln + lnx Combine like terms: -13ln + 48ln = 35ln 35ln + 2lnx = -48ln + 48ln + lnx Combine like terms: -48ln + 48ln = 0 35ln + 2lnx = 0 + lnx 35ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 35ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 35ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 35ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(35 + 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 '(35 + x)' equal to zero and attempt to solve: Simplifying 35 + x = 0 Solving 35 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + x = 0 + -35 x = 0 + -35 Combine like terms: 0 + -35 = -35 x = -35 Add '-1x' to each side of the equation. x + -1x = -35 + -1x Combine like terms: x + -1x = 0 0 = -35 + -1x Simplifying 0 = -35 + -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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