ln(4x-1)+ln(x-1)=ln(1)

Solution for ln(4x-1)+ln(x-1)=ln(1) equation:

Simplifying
ln(4x + -1) + ln(x + -1) = ln(1)

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

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

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

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

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

Reorder the terms for easier multiplication:
-2ln + 5lnx = 1ln

Solving
-2ln + 5lnx = 1ln

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-2ln + -1ln + 5lnx = 1ln + -1ln

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

Combine like terms: 1ln + -1ln = 0
-3ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 5x) = 0

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 '(-3 + 5x)' equal to zero and attempt to solve:

Simplifying
-3 + 5x = 0

Solving
-3 + 5x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5x = 0 + 3
5x = 0 + 3

Combine like terms: 0 + 3 = 3
5x = 3

Add '-5x' to each side of the equation.
5x + -5x = 3 + -5x

Combine like terms: 5x + -5x = 0
0 = 3 + -5x

Simplifying
0 = 3 + -5x

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.