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Simplifying ln(7x + 25) = ln(4x + -5) Reorder the terms: ln(25 + 7x) = ln(4x + -5) (25 * ln + 7x * ln) = ln(4x + -5) (25ln + 7lnx) = ln(4x + -5) Reorder the terms: 25ln + 7lnx = ln(-5 + 4x) 25ln + 7lnx = (-5 * ln + 4x * ln) 25ln + 7lnx = (-5ln + 4lnx) Solving 25ln + 7lnx = -5ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 25ln + 5ln + 7lnx = -5ln + 5ln + 4lnx Combine like terms: 25ln + 5ln = 30ln 30ln + 7lnx = -5ln + 5ln + 4lnx Combine like terms: -5ln + 5ln = 0 30ln + 7lnx = 0 + 4lnx 30ln + 7lnx = 4lnx Add '-4lnx' to each side of the equation. 30ln + 7lnx + -4lnx = 4lnx + -4lnx Combine like terms: 7lnx + -4lnx = 3lnx 30ln + 3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 30ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(10 + x) = 0 Ignore the factor 3.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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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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