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.