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

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


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

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

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

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

Solving for variable 'n'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = 2L + 2l + 3lx + -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}

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