Ln(2x-6)=ln(5x-6)

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Solution for Ln(2x-6)=ln(5x-6) equation: 


Simplifying
Ln(2x + -6) = ln(5x + -6)

Reorder the terms:
nL(-6 + 2x) = ln(5x + -6)
(-6 * nL + 2x * nL) = ln(5x + -6)
(-6nL + 2nxL) = ln(5x + -6)

Reorder the terms:
-6nL + 2nxL = ln(-6 + 5x)
-6nL + 2nxL = (-6 * ln + 5x * ln)
-6nL + 2nxL = (-6ln + 5lnx)

Solving
-6nL + 2nxL = -6ln + 5lnx

Solving for variable 'n'.

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

Add '6ln' to each side of the equation.
-6nL + 6ln + 2nxL = -6ln + 6ln + 5lnx

Reorder the terms:
6ln + -6nL + 2nxL = -6ln + 6ln + 5lnx

Combine like terms: -6ln + 6ln = 0
6ln + -6nL + 2nxL = 0 + 5lnx
6ln + -6nL + 2nxL = 5lnx

Add '-5lnx' to each side of the equation.
6ln + -6nL + -5lnx + 2nxL = 5lnx + -5lnx

Reorder the terms:
6ln + -5lnx + -6nL + 2nxL = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
6ln + -5lnx + -6nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(6l + -5lx + -6L + 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 '(6l + -5lx + -6L + 2xL)' equal to zero and attempt to solve:

Simplifying
6l + -5lx + -6L + 2xL = 0

Reorder the terms:
-6L + 6l + -5lx + 2xL = 0

Solving
-6L + 6l + -5lx + 2xL = 0

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

Add '6L' to each side of the equation.
-6L + 6l + -5lx + 6L + 2xL = 0 + 6L

Reorder the terms:
-6L + 6L + 6l + -5lx + 2xL = 0 + 6L

Combine like terms: -6L + 6L = 0
0 + 6l + -5lx + 2xL = 0 + 6L
6l + -5lx + 2xL = 0 + 6L
Remove the zero:
6l + -5lx + 2xL = 6L

Add '-6l' to each side of the equation.
6l + -5lx + -6l + 2xL = 6L + -6l

Reorder the terms:
6l + -6l + -5lx + 2xL = 6L + -6l

Combine like terms: 6l + -6l = 0
0 + -5lx + 2xL = 6L + -6l
-5lx + 2xL = 6L + -6l

Add '5lx' to each side of the equation.
-5lx + 5lx + 2xL = 6L + -6l + 5lx

Combine like terms: -5lx + 5lx = 0
0 + 2xL = 6L + -6l + 5lx
2xL = 6L + -6l + 5lx

Add '-2xL' to each side of the equation.
2xL + -2xL = 6L + -6l + 5lx + -2xL

Combine like terms: 2xL + -2xL = 0
0 = 6L + -6l + 5lx + -2xL

Simplifying
0 = 6L + -6l + 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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