Ln(x-2)=ln(10x)

Solution for Ln(x-2)=ln(10x) equation:

Simplifying
Ln(x + -2) = ln(10x)

Reorder the terms:
nL(-2 + x) = ln(10x)
(-2 * nL + x * nL) = ln(10x)
(-2nL + nxL) = ln(10x)

Remove parenthesis around (10x)
-2nL + nxL = ln * 10x

Reorder the terms for easier multiplication:
-2nL + nxL = 10ln * x

Multiply ln * x
-2nL + nxL = 10lnx

Solving
-2nL + nxL = 10lnx

Solving for variable 'n'.

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

Add '-10lnx' to each side of the equation.
-2nL + -10lnx + nxL = 10lnx + -10lnx

Reorder the terms:
-10lnx + -2nL + nxL = 10lnx + -10lnx

Combine like terms: 10lnx + -10lnx = 0
-10lnx + -2nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-10lx + -2L + xL) = 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 '(-10lx + -2L + xL)' equal to zero and attempt to solve:

Simplifying
-10lx + -2L + xL = 0

Reorder the terms:
-2L + -10lx + xL = 0

Solving
-2L + -10lx + xL = 0

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

Add '2L' to each side of the equation.
-2L + -10lx + 2L + xL = 0 + 2L

Reorder the terms:
-2L + 2L + -10lx + xL = 0 + 2L

Combine like terms: -2L + 2L = 0
0 + -10lx + xL = 0 + 2L
-10lx + xL = 0 + 2L
Remove the zero:
-10lx + xL = 2L

Add '10lx' to each side of the equation.
-10lx + 10lx + xL = 2L + 10lx

Combine like terms: -10lx + 10lx = 0
0 + xL = 2L + 10lx
xL = 2L + 10lx

Add '-1xL' to each side of the equation.
xL + -1xL = 2L + 10lx + -1xL

Combine like terms: xL + -1xL = 0
0 = 2L + 10lx + -1xL

Simplifying
0 = 2L + 10lx + -1xL

The solution to this equation could not be determined.

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