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Simplifying ln(7x + 37) = ln(2x + -8) Reorder the terms: ln(37 + 7x) = ln(2x + -8) (37 * ln + 7x * ln) = ln(2x + -8) (37ln + 7lnx) = ln(2x + -8) Reorder the terms: 37ln + 7lnx = ln(-8 + 2x) 37ln + 7lnx = (-8 * ln + 2x * ln) 37ln + 7lnx = (-8ln + 2lnx) Solving 37ln + 7lnx = -8ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 37ln + 8ln + 7lnx = -8ln + 8ln + 2lnx Combine like terms: 37ln + 8ln = 45ln 45ln + 7lnx = -8ln + 8ln + 2lnx Combine like terms: -8ln + 8ln = 0 45ln + 7lnx = 0 + 2lnx 45ln + 7lnx = 2lnx Add '-2lnx' to each side of the equation. 45ln + 7lnx + -2lnx = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx 45ln + 5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 45ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(9 + x) = 0 Ignore the factor 5.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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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