Ln(x-3)=ln(4x+1)

Solution for Ln(x-3)=ln(4x+1) equation:

Simplifying
Ln(x + -3) = ln(4x + 1)

Reorder the terms:
nL(-3 + x) = ln(4x + 1)
(-3 * nL + x * nL) = ln(4x + 1)
(-3nL + nxL) = ln(4x + 1)

Reorder the terms:
-3nL + nxL = ln(1 + 4x)
-3nL + nxL = (1 * ln + 4x * ln)
-3nL + nxL = (1ln + 4lnx)

Solving
-3nL + nxL = 1ln + 4lnx

Solving for variable 'n'.

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

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

Reorder the terms:
-1ln + -3nL + nxL = 1ln + -1ln + 4lnx

Combine like terms: 1ln + -1ln = 0
-1ln + -3nL + nxL = 0 + 4lnx
-1ln + -3nL + nxL = 4lnx

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

Reorder the terms:
-1ln + -4lnx + -3nL + nxL = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-1ln + -4lnx + -3nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1l + -4lx + -3L + xL) = 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 '(-1l + -4lx + -3L + xL)' equal to zero and attempt to solve:

Simplifying
-1l + -4lx + -3L + xL = 0

Reorder the terms:
-3L + -1l + -4lx + xL = 0

Solving
-3L + -1l + -4lx + xL = 0

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

Add '3L' to each side of the equation.
-3L + -1l + -4lx + 3L + xL = 0 + 3L

Reorder the terms:
-3L + 3L + -1l + -4lx + xL = 0 + 3L

Combine like terms: -3L + 3L = 0
0 + -1l + -4lx + xL = 0 + 3L
-1l + -4lx + xL = 0 + 3L
Remove the zero:
-1l + -4lx + xL = 3L

Add 'l' to each side of the equation.
-1l + -4lx + l + xL = 3L + l

Reorder the terms:
-1l + l + -4lx + xL = 3L + l

Combine like terms: -1l + l = 0
0 + -4lx + xL = 3L + l
-4lx + xL = 3L + l

Add '4lx' to each side of the equation.
-4lx + 4lx + xL = 3L + l + 4lx

Combine like terms: -4lx + 4lx = 0
0 + xL = 3L + l + 4lx
xL = 3L + l + 4lx

Add '-1xL' to each side of the equation.
xL + -1xL = 3L + l + 4lx + -1xL

Combine like terms: xL + -1xL = 0
0 = 3L + l + 4lx + -1xL

Simplifying
0 = 3L + l + 4lx + -1xL

The solution to this equation could not be determined.

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