Ln(2x)=ln(9x-10)

Solution for Ln(2x)=ln(9x-10) equation:

Simplifying
Ln(2x) = ln(9x + -10)

Remove parenthesis around (2x)
nL * 2x = ln(9x + -10)

Reorder the terms for easier multiplication:
2nL * x = ln(9x + -10)

Multiply nL * x
2nxL = ln(9x + -10)

Reorder the terms:
2nxL = ln(-10 + 9x)
2nxL = (-10 * ln + 9x * ln)
2nxL = (-10ln + 9lnx)

Solving
2nxL = -10ln + 9lnx

Solving for variable 'n'.

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

Add '10ln' to each side of the equation.
10ln + 2nxL = -10ln + 10ln + 9lnx

Combine like terms: -10ln + 10ln = 0
10ln + 2nxL = 0 + 9lnx
10ln + 2nxL = 9lnx

Add '-9lnx' to each side of the equation.
10ln + -9lnx + 2nxL = 9lnx + -9lnx

Combine like terms: 9lnx + -9lnx = 0
10ln + -9lnx + 2nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(10l + -9lx + 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 '(10l + -9lx + 2xL)' equal to zero and attempt to solve:

Simplifying
10l + -9lx + 2xL = 0

Solving
10l + -9lx + 2xL = 0

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

Add '-10l' to each side of the equation.
10l + -9lx + -10l + 2xL = 0 + -10l

Reorder the terms:
10l + -10l + -9lx + 2xL = 0 + -10l

Combine like terms: 10l + -10l = 0
0 + -9lx + 2xL = 0 + -10l
-9lx + 2xL = 0 + -10l
Remove the zero:
-9lx + 2xL = -10l

Add '9lx' to each side of the equation.
-9lx + 9lx + 2xL = -10l + 9lx

Combine like terms: -9lx + 9lx = 0
0 + 2xL = -10l + 9lx
2xL = -10l + 9lx

Add '-2xL' to each side of the equation.
2xL + -2xL = -10l + 9lx + -2xL

Combine like terms: 2xL + -2xL = 0
0 = -10l + 9lx + -2xL

Simplifying
0 = -10l + 9lx + -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}