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

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

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

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

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

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

Solving for variable 'n'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -2L + 5l + 2lx + -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}