Ln(4x-1)=ln(x-6)

Solution for Ln(4x-1)=ln(x-6) equation:

Simplifying
Ln(4x + -1) = ln(x + -6)

Reorder the terms:
nL(-1 + 4x) = ln(x + -6)
(-1 * nL + 4x * nL) = ln(x + -6)
(-1nL + 4nxL) = ln(x + -6)

Reorder the terms:
-1nL + 4nxL = ln(-6 + x)
-1nL + 4nxL = (-6 * ln + x * ln)
-1nL + 4nxL = (-6ln + lnx)

Solving
-1nL + 4nxL = -6ln + lnx

Solving for variable 'n'.

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

Add '6ln' to each side of the equation.
-1nL + 6ln + 4nxL = -6ln + 6ln + lnx

Reorder the terms:
6ln + -1nL + 4nxL = -6ln + 6ln + lnx

Combine like terms: -6ln + 6ln = 0
6ln + -1nL + 4nxL = 0 + lnx
6ln + -1nL + 4nxL = lnx

Add '-1lnx' to each side of the equation.
6ln + -1nL + -1lnx + 4nxL = lnx + -1lnx

Reorder the terms:
6ln + -1lnx + -1nL + 4nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln + -1lnx + -1nL + 4nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(6l + -1lx + -1L + 4xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(6l + -1lx + -1L + 4xL)' equal to zero and attempt to solve:

Simplifying
6l + -1lx + -1L + 4xL = 0

Reorder the terms:
-1L + 6l + -1lx + 4xL = 0

Solving
-1L + 6l + -1lx + 4xL = 0

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

Add 'L' to each side of the equation.
-1L + 6l + -1lx + L + 4xL = 0 + L

Reorder the terms:
-1L + L + 6l + -1lx + 4xL = 0 + L

Combine like terms: -1L + L = 0
0 + 6l + -1lx + 4xL = 0 + L
6l + -1lx + 4xL = 0 + L
Remove the zero:
6l + -1lx + 4xL = L

Add '-6l' to each side of the equation.
6l + -1lx + -6l + 4xL = L + -6l

Reorder the terms:
6l + -6l + -1lx + 4xL = L + -6l

Combine like terms: 6l + -6l = 0
0 + -1lx + 4xL = L + -6l
-1lx + 4xL = L + -6l

Add 'lx' to each side of the equation.
-1lx + lx + 4xL = L + -6l + lx

Combine like terms: -1lx + lx = 0
0 + 4xL = L + -6l + lx
4xL = L + -6l + lx

Add '-4xL' to each side of the equation.
4xL + -4xL = L + -6l + lx + -4xL

Combine like terms: 4xL + -4xL = 0
0 = L + -6l + lx + -4xL

Simplifying
0 = L + -6l + lx + -4xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}