Ln(x+2)=ln(9x-3)

Solution for Ln(x+2)=ln(9x-3) equation:

Simplifying
Ln(x + 2) = ln(9x + -3)

Reorder the terms:
nL(2 + x) = ln(9x + -3)
(2 * nL + x * nL) = ln(9x + -3)
(2nL + nxL) = ln(9x + -3)

Reorder the terms:
2nL + nxL = ln(-3 + 9x)
2nL + nxL = (-3 * ln + 9x * ln)
2nL + nxL = (-3ln + 9lnx)

Solving
2nL + nxL = -3ln + 9lnx

Solving for variable 'n'.

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

Add '3ln' to each side of the equation.
2nL + 3ln + nxL = -3ln + 3ln + 9lnx

Reorder the terms:
3ln + 2nL + nxL = -3ln + 3ln + 9lnx

Combine like terms: -3ln + 3ln = 0
3ln + 2nL + nxL = 0 + 9lnx
3ln + 2nL + nxL = 9lnx

Add '-9lnx' to each side of the equation.
3ln + 2nL + -9lnx + nxL = 9lnx + -9lnx

Reorder the terms:
3ln + -9lnx + 2nL + nxL = 9lnx + -9lnx

Combine like terms: 9lnx + -9lnx = 0
3ln + -9lnx + 2nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3l + -9lx + 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 '(3l + -9lx + 2L + xL)' equal to zero and attempt to solve:

Simplifying
3l + -9lx + 2L + xL = 0

Reorder the terms:
2L + 3l + -9lx + xL = 0

Solving
2L + 3l + -9lx + 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 + 3l + -9lx + -2L + xL = 0 + -2L

Reorder the terms:
2L + -2L + 3l + -9lx + xL = 0 + -2L

Combine like terms: 2L + -2L = 0
0 + 3l + -9lx + xL = 0 + -2L
3l + -9lx + xL = 0 + -2L
Remove the zero:
3l + -9lx + xL = -2L

Add '-3l' to each side of the equation.
3l + -9lx + -3l + xL = -2L + -3l

Reorder the terms:
3l + -3l + -9lx + xL = -2L + -3l

Combine like terms: 3l + -3l = 0
0 + -9lx + xL = -2L + -3l
-9lx + xL = -2L + -3l

Add '9lx' to each side of the equation.
-9lx + 9lx + xL = -2L + -3l + 9lx

Combine like terms: -9lx + 9lx = 0
0 + xL = -2L + -3l + 9lx
xL = -2L + -3l + 9lx

Add '-1xL' to each side of the equation.
xL + -1xL = -2L + -3l + 9lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -2L + -3l + 9lx + -1xL

Simplifying
0 = -2L + -3l + 9lx + -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}