Ln(5-2x)=ln(5x+3)

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Solution for Ln(5-2x)=ln(5x+3) equation: 


Simplifying
Ln(5 + -2x) = ln(5x + 3)
(5 * nL + -2x * nL) = ln(5x + 3)
(5nL + -2nxL) = ln(5x + 3)

Reorder the terms:
5nL + -2nxL = ln(3 + 5x)
5nL + -2nxL = (3 * ln + 5x * ln)
5nL + -2nxL = (3ln + 5lnx)

Solving
5nL + -2nxL = 3ln + 5lnx

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.
5nL + -3ln + -2nxL = 3ln + -3ln + 5lnx

Reorder the terms:
-3ln + 5nL + -2nxL = 3ln + -3ln + 5lnx

Combine like terms: 3ln + -3ln = 0
-3ln + 5nL + -2nxL = 0 + 5lnx
-3ln + 5nL + -2nxL = 5lnx

Add '-5lnx' to each side of the equation.
-3ln + 5nL + -5lnx + -2nxL = 5lnx + -5lnx

Reorder the terms:
-3ln + -5lnx + 5nL + -2nxL = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-3ln + -5lnx + 5nL + -2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3l + -5lx + 5L + -2xL) = 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 + -5lx + 5L + -2xL)' equal to zero and attempt to solve:

Simplifying
-3l + -5lx + 5L + -2xL = 0

Reorder the terms:
5L + -3l + -5lx + -2xL = 0

Solving
5L + -3l + -5lx + -2xL = 0

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

Add '-5L' to each side of the equation.
5L + -3l + -5lx + -5L + -2xL = 0 + -5L

Reorder the terms:
5L + -5L + -3l + -5lx + -2xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + -3l + -5lx + -2xL = 0 + -5L
-3l + -5lx + -2xL = 0 + -5L
Remove the zero:
-3l + -5lx + -2xL = -5L

Add '3l' to each side of the equation.
-3l + -5lx + 3l + -2xL = -5L + 3l

Reorder the terms:
-3l + 3l + -5lx + -2xL = -5L + 3l

Combine like terms: -3l + 3l = 0
0 + -5lx + -2xL = -5L + 3l
-5lx + -2xL = -5L + 3l

Add '5lx' to each side of the equation.
-5lx + 5lx + -2xL = -5L + 3l + 5lx

Combine like terms: -5lx + 5lx = 0
0 + -2xL = -5L + 3l + 5lx
-2xL = -5L + 3l + 5lx

Add '2xL' to each side of the equation.
-2xL + 2xL = -5L + 3l + 5lx + 2xL

Combine like terms: -2xL + 2xL = 0
0 = -5L + 3l + 5lx + 2xL

Simplifying
0 = -5L + 3l + 5lx + 2xL

The solution to this equation could not be determined.

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

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