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Simplifying ln(5x + 1) = 2(ln(4x + -1)) Reorder the terms: ln(1 + 5x) = 2(ln(4x + -1)) (1 * ln + 5x * ln) = 2(ln(4x + -1)) (1ln + 5lnx) = 2(ln(4x + -1)) Reorder the terms: 1ln + 5lnx = 2(ln(-1 + 4x)) 1ln + 5lnx = 2((-1 * ln + 4x * ln)) 1ln + 5lnx = 2((-1ln + 4lnx)) 1ln + 5lnx = (-1ln * 2 + 4lnx * 2) 1ln + 5lnx = (-2ln + 8lnx) Solving 1ln + 5lnx = -2ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 1ln + 2ln + 5lnx = -2ln + 2ln + 8lnx Combine like terms: 1ln + 2ln = 3ln 3ln + 5lnx = -2ln + 2ln + 8lnx Combine like terms: -2ln + 2ln = 0 3ln + 5lnx = 0 + 8lnx 3ln + 5lnx = 8lnx Add '-8lnx' to each side of the equation. 3ln + 5lnx + -8lnx = 8lnx + -8lnx Combine like terms: 5lnx + -8lnx = -3lnx 3ln + -3lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 3ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(1 + -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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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