Ln(5x+4)=ln(3-x)

Solution for Ln(5x+4)=ln(3-x) equation:

Simplifying
Ln(5x + 4) = ln(3 + -1x)

Reorder the terms:
nL(4 + 5x) = ln(3 + -1x)
(4 * nL + 5x * nL) = ln(3 + -1x)
(4nL + 5nxL) = ln(3 + -1x)
4nL + 5nxL = (3 * ln + -1x * ln)
4nL + 5nxL = (3ln + -1lnx)

Solving
4nL + 5nxL = 3ln + -1lnx

Solving for variable 'n'.

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

Add '-3ln' to each side of the equation.
4nL + -3ln + 5nxL = 3ln + -3ln + -1lnx

Reorder the terms:
-3ln + 4nL + 5nxL = 3ln + -3ln + -1lnx

Combine like terms: 3ln + -3ln = 0
-3ln + 4nL + 5nxL = 0 + -1lnx
-3ln + 4nL + 5nxL = -1lnx

Add 'lnx' to each side of the equation.
-3ln + 4nL + lnx + 5nxL = -1lnx + lnx

Reorder the terms:
-3ln + lnx + 4nL + 5nxL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-3ln + lnx + 4nL + 5nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3l + lx + 4L + 5xL) = 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 '(-3l + lx + 4L + 5xL)' equal to zero and attempt to solve:

Simplifying
-3l + lx + 4L + 5xL = 0

Reorder the terms:
4L + -3l + lx + 5xL = 0

Solving
4L + -3l + lx + 5xL = 0

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

Add '-4L' to each side of the equation.
4L + -3l + lx + -4L + 5xL = 0 + -4L

Reorder the terms:
4L + -4L + -3l + lx + 5xL = 0 + -4L

Combine like terms: 4L + -4L = 0
0 + -3l + lx + 5xL = 0 + -4L
-3l + lx + 5xL = 0 + -4L
Remove the zero:
-3l + lx + 5xL = -4L

Add '3l' to each side of the equation.
-3l + lx + 3l + 5xL = -4L + 3l

Reorder the terms:
-3l + 3l + lx + 5xL = -4L + 3l

Combine like terms: -3l + 3l = 0
0 + lx + 5xL = -4L + 3l
lx + 5xL = -4L + 3l

Add '-1lx' to each side of the equation.
lx + -1lx + 5xL = -4L + 3l + -1lx

Combine like terms: lx + -1lx = 0
0 + 5xL = -4L + 3l + -1lx
5xL = -4L + 3l + -1lx

Add '-5xL' to each side of the equation.
5xL + -5xL = -4L + 3l + -1lx + -5xL

Combine like terms: 5xL + -5xL = 0
0 = -4L + 3l + -1lx + -5xL

Simplifying
0 = -4L + 3l + -1lx + -5xL

The solution to this equation could not be determined.

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