Ln(x+5)=ln(9x-5)

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Solution for Ln(x+5)=ln(9x-5) equation: 


Simplifying
Ln(x + 5) = ln(9x + -5)

Reorder the terms:
nL(5 + x) = ln(9x + -5)
(5 * nL + x * nL) = ln(9x + -5)
(5nL + nxL) = ln(9x + -5)

Reorder the terms:
5nL + nxL = ln(-5 + 9x)
5nL + nxL = (-5 * ln + 9x * ln)
5nL + nxL = (-5ln + 9lnx)

Solving
5nL + nxL = -5ln + 9lnx

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.
5nL + 5ln + nxL = -5ln + 5ln + 9lnx

Reorder the terms:
5ln + 5nL + nxL = -5ln + 5ln + 9lnx

Combine like terms: -5ln + 5ln = 0
5ln + 5nL + nxL = 0 + 9lnx
5ln + 5nL + nxL = 9lnx

Add '-9lnx' to each side of the equation.
5ln + 5nL + -9lnx + nxL = 9lnx + -9lnx

Reorder the terms:
5ln + -9lnx + 5nL + nxL = 9lnx + -9lnx

Combine like terms: 9lnx + -9lnx = 0
5ln + -9lnx + 5nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(5l + -9lx + 5L + 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 '(5l + -9lx + 5L + xL)' equal to zero and attempt to solve:

Simplifying
5l + -9lx + 5L + xL = 0

Reorder the terms:
5L + 5l + -9lx + xL = 0

Solving
5L + 5l + -9lx + xL = 0

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

Add '-5L' to each side of the equation.
5L + 5l + -9lx + -5L + xL = 0 + -5L

Reorder the terms:
5L + -5L + 5l + -9lx + xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + 5l + -9lx + xL = 0 + -5L
5l + -9lx + xL = 0 + -5L
Remove the zero:
5l + -9lx + xL = -5L

Add '-5l' to each side of the equation.
5l + -9lx + -5l + xL = -5L + -5l

Reorder the terms:
5l + -5l + -9lx + xL = -5L + -5l

Combine like terms: 5l + -5l = 0
0 + -9lx + xL = -5L + -5l
-9lx + xL = -5L + -5l

Add '9lx' to each side of the equation.
-9lx + 9lx + xL = -5L + -5l + 9lx

Combine like terms: -9lx + 9lx = 0
0 + xL = -5L + -5l + 9lx
xL = -5L + -5l + 9lx

Add '-1xL' to each side of the equation.
xL + -1xL = -5L + -5l + 9lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -5L + -5l + 9lx + -1xL

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

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