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Simplifying
ln(5) * x + -1ln(2x + -1) = ln(4)

Reorder the terms for easier multiplication:
5ln * x + -1ln(2x + -1) = ln(4)

Multiply ln * x
5lnx + -1ln(2x + -1) = ln(4)

Reorder the terms:
5lnx + -1ln(-1 + 2x) = ln(4)
5lnx + (-1 * -1ln + 2x * -1ln) = ln(4)
5lnx + (1ln + -2lnx) = ln(4)

Reorder the terms:
1ln + 5lnx + -2lnx = ln(4)

Combine like terms: 5lnx + -2lnx = 3lnx
1ln + 3lnx = ln(4)

Reorder the terms for easier multiplication:
1ln + 3lnx = 4ln

Solving
1ln + 3lnx = 4ln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-4ln' to each side of the equation.
1ln + -4ln + 3lnx = 4ln + -4ln

Combine like terms: 1ln + -4ln = -3ln
-3ln + 3lnx = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
-3ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-1 + 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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