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Simplifying ln(x + 5) + ln(x + 2) = ln(x + 37) Reorder the terms: ln(5 + x) + ln(x + 2) = ln(x + 37) (5 * ln + x * ln) + ln(x + 2) = ln(x + 37) (5ln + lnx) + ln(x + 2) = ln(x + 37) Reorder the terms: 5ln + lnx + ln(2 + x) = ln(x + 37) 5ln + lnx + (2 * ln + x * ln) = ln(x + 37) 5ln + lnx + (2ln + lnx) = ln(x + 37) Reorder the terms: 5ln + 2ln + lnx + lnx = ln(x + 37) Combine like terms: 5ln + 2ln = 7ln 7ln + lnx + lnx = ln(x + 37) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(x + 37) Reorder the terms: 7ln + 2lnx = ln(37 + x) 7ln + 2lnx = (37 * ln + x * ln) 7ln + 2lnx = (37ln + lnx) Solving 7ln + 2lnx = 37ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-37ln' to each side of the equation. 7ln + -37ln + 2lnx = 37ln + -37ln + lnx Combine like terms: 7ln + -37ln = -30ln -30ln + 2lnx = 37ln + -37ln + lnx Combine like terms: 37ln + -37ln = 0 -30ln + 2lnx = 0 + lnx -30ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -30ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -30ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -30ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-30 + 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 '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Add '-1x' to each side of the equation. x + -1x = 30 + -1x Combine like terms: x + -1x = 0 0 = 30 + -1x Simplifying 0 = 30 + -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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