Ln(x+5)=ln(7x-5)

Solution for Ln(x+5)=ln(7x-5) equation:

Simplifying
Ln(x + 5) = ln(7x + -5)

Reorder the terms:
nL(5 + x) = ln(7x + -5)
(5 * nL + x * nL) = ln(7x + -5)
(5nL + nxL) = ln(7x + -5)

Reorder the terms:
5nL + nxL = ln(-5 + 7x)
5nL + nxL = (-5 * ln + 7x * ln)
5nL + nxL = (-5ln + 7lnx)

Solving
5nL + nxL = -5ln + 7lnx

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 + 7lnx

Reorder the terms:
5ln + 5nL + nxL = -5ln + 5ln + 7lnx

Combine like terms: -5ln + 5ln = 0
5ln + 5nL + nxL = 0 + 7lnx
5ln + 5nL + nxL = 7lnx

Add '-7lnx' to each side of the equation.
5ln + 5nL + -7lnx + nxL = 7lnx + -7lnx

Reorder the terms:
5ln + -7lnx + 5nL + nxL = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
5ln + -7lnx + 5nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(5l + -7lx + 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 + -7lx + 5L + xL)' equal to zero and attempt to solve:

Simplifying
5l + -7lx + 5L + xL = 0

Reorder the terms:
5L + 5l + -7lx + xL = 0

Solving
5L + 5l + -7lx + 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 + -7lx + -5L + xL = 0 + -5L

Reorder the terms:
5L + -5L + 5l + -7lx + xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + 5l + -7lx + xL = 0 + -5L
5l + -7lx + xL = 0 + -5L
Remove the zero:
5l + -7lx + xL = -5L

Add '-5l' to each side of the equation.
5l + -7lx + -5l + xL = -5L + -5l

Reorder the terms:
5l + -5l + -7lx + xL = -5L + -5l

Combine like terms: 5l + -5l = 0
0 + -7lx + xL = -5L + -5l
-7lx + xL = -5L + -5l

Add '7lx' to each side of the equation.
-7lx + 7lx + xL = -5L + -5l + 7lx

Combine like terms: -7lx + 7lx = 0
0 + xL = -5L + -5l + 7lx
xL = -5L + -5l + 7lx

Add '-1xL' to each side of the equation.
xL + -1xL = -5L + -5l + 7lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -5L + -5l + 7lx + -1xL

Simplifying
0 = -5L + -5l + 7lx + -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}