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Simplifying ln(7x + 15) = ln(4x + -9) Reorder the terms: ln(15 + 7x) = ln(4x + -9) (15 * ln + 7x * ln) = ln(4x + -9) (15ln + 7lnx) = ln(4x + -9) Reorder the terms: 15ln + 7lnx = ln(-9 + 4x) 15ln + 7lnx = (-9 * ln + 4x * ln) 15ln + 7lnx = (-9ln + 4lnx) Solving 15ln + 7lnx = -9ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '9ln' to each side of the equation. 15ln + 9ln + 7lnx = -9ln + 9ln + 4lnx Combine like terms: 15ln + 9ln = 24ln 24ln + 7lnx = -9ln + 9ln + 4lnx Combine like terms: -9ln + 9ln = 0 24ln + 7lnx = 0 + 4lnx 24ln + 7lnx = 4lnx Add '-4lnx' to each side of the equation. 24ln + 7lnx + -4lnx = 4lnx + -4lnx Combine like terms: 7lnx + -4lnx = 3lnx 24ln + 3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 24ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(8 + 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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