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Simplifying ln(4x + 2) = ln(7x + -10) Reorder the terms: ln(2 + 4x) = ln(7x + -10) (2 * ln + 4x * ln) = ln(7x + -10) (2ln + 4lnx) = ln(7x + -10) Reorder the terms: 2ln + 4lnx = ln(-10 + 7x) 2ln + 4lnx = (-10 * ln + 7x * ln) 2ln + 4lnx = (-10ln + 7lnx) Solving 2ln + 4lnx = -10ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '10ln' to each side of the equation. 2ln + 10ln + 4lnx = -10ln + 10ln + 7lnx Combine like terms: 2ln + 10ln = 12ln 12ln + 4lnx = -10ln + 10ln + 7lnx Combine like terms: -10ln + 10ln = 0 12ln + 4lnx = 0 + 7lnx 12ln + 4lnx = 7lnx Add '-7lnx' to each side of the equation. 12ln + 4lnx + -7lnx = 7lnx + -7lnx Combine like terms: 4lnx + -7lnx = -3lnx 12ln + -3lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 12ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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