ln(x)+ln(x-3)=lm(7x)

Solution for ln(x)+ln(x-3)=lm(7x) equation:

Simplifying
ln(x) + ln(x + -3) = lm(7x)

Multiply ln * x
lnx + ln(x + -3) = lm(7x)

Reorder the terms:
lnx + ln(-3 + x) = lm(7x)
lnx + (-3 * ln + x * ln) = lm(7x)
lnx + (-3ln + lnx) = lm(7x)

Reorder the terms:
-3ln + lnx + lnx = lm(7x)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = lm(7x)

Remove parenthesis around (7x)
-3ln + 2lnx = lm * 7x

Reorder the terms for easier multiplication:
-3ln + 2lnx = 7lm * x

Multiply lm * x
-3ln + 2lnx = 7lmx

Solving
-3ln + 2lnx = 7lmx

Solving for variable 'l'.

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

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

Reorder the terms:
-7lmx + -3ln + 2lnx = 7lmx + -7lmx

Combine like terms: 7lmx + -7lmx = 0
-7lmx + -3ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'l'.
l(-7mx + -3n + 2nx) = 0

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

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0
Subproblem 2
Set the factor '(-7mx + -3n + 2nx)' equal to zero and attempt to solve:

Simplifying
-7mx + -3n + 2nx = 0

Solving
-7mx + -3n + 2nx = 0

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

Add '7mx' to each side of the equation.
-7mx + -3n + 7mx + 2nx = 0 + 7mx

Reorder the terms:
-7mx + 7mx + -3n + 2nx = 0 + 7mx

Combine like terms: -7mx + 7mx = 0
0 + -3n + 2nx = 0 + 7mx
-3n + 2nx = 0 + 7mx
Remove the zero:
-3n + 2nx = 7mx

Add '3n' to each side of the equation.
-3n + 3n + 2nx = 7mx + 3n

Combine like terms: -3n + 3n = 0
0 + 2nx = 7mx + 3n
2nx = 7mx + 3n

Add '-2nx' to each side of the equation.
2nx + -2nx = 7mx + 3n + -2nx

Combine like terms: 2nx + -2nx = 0
0 = 7mx + 3n + -2nx

Simplifying
0 = 7mx + 3n + -2nx

The solution to this equation could not be determined.

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