Ln(7x-3)=ln(2x-4)

Solution for Ln(7x-3)=ln(2x-4) equation:

Simplifying
Ln(7x + -3) = ln(2x + -4)

Reorder the terms:
nL(-3 + 7x) = ln(2x + -4)
(-3 * nL + 7x * nL) = ln(2x + -4)
(-3nL + 7nxL) = ln(2x + -4)

Reorder the terms:
-3nL + 7nxL = ln(-4 + 2x)
-3nL + 7nxL = (-4 * ln + 2x * ln)
-3nL + 7nxL = (-4ln + 2lnx)

Solving
-3nL + 7nxL = -4ln + 2lnx

Solving for variable 'n'.

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

Add '4ln' to each side of the equation.
-3nL + 4ln + 7nxL = -4ln + 4ln + 2lnx

Reorder the terms:
4ln + -3nL + 7nxL = -4ln + 4ln + 2lnx

Combine like terms: -4ln + 4ln = 0
4ln + -3nL + 7nxL = 0 + 2lnx
4ln + -3nL + 7nxL = 2lnx

Add '-2lnx' to each side of the equation.
4ln + -3nL + -2lnx + 7nxL = 2lnx + -2lnx

Reorder the terms:
4ln + -2lnx + -3nL + 7nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
4ln + -2lnx + -3nL + 7nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(4l + -2lx + -3L + 7xL) = 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 '(4l + -2lx + -3L + 7xL)' equal to zero and attempt to solve:

Simplifying
4l + -2lx + -3L + 7xL = 0

Reorder the terms:
-3L + 4l + -2lx + 7xL = 0

Solving
-3L + 4l + -2lx + 7xL = 0

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

Add '3L' to each side of the equation.
-3L + 4l + -2lx + 3L + 7xL = 0 + 3L

Reorder the terms:
-3L + 3L + 4l + -2lx + 7xL = 0 + 3L

Combine like terms: -3L + 3L = 0
0 + 4l + -2lx + 7xL = 0 + 3L
4l + -2lx + 7xL = 0 + 3L
Remove the zero:
4l + -2lx + 7xL = 3L

Add '-4l' to each side of the equation.
4l + -2lx + -4l + 7xL = 3L + -4l

Reorder the terms:
4l + -4l + -2lx + 7xL = 3L + -4l

Combine like terms: 4l + -4l = 0
0 + -2lx + 7xL = 3L + -4l
-2lx + 7xL = 3L + -4l

Add '2lx' to each side of the equation.
-2lx + 2lx + 7xL = 3L + -4l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 7xL = 3L + -4l + 2lx
7xL = 3L + -4l + 2lx

Add '-7xL' to each side of the equation.
7xL + -7xL = 3L + -4l + 2lx + -7xL

Combine like terms: 7xL + -7xL = 0
0 = 3L + -4l + 2lx + -7xL

Simplifying
0 = 3L + -4l + 2lx + -7xL

The solution to this equation could not be determined.

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