Ln(x)=ln(6)-ln(x+5)

Solution for Ln(x)=ln(6)-ln(x+5) equation:

Simplifying
Ln(x) = ln(6) + -1ln(x + 5)

Multiply nL * x
nxL = ln(6) + -1ln(x + 5)

Reorder the terms for easier multiplication:
nxL = 6ln + -1ln(x + 5)

Reorder the terms:
nxL = 6ln + -1ln(5 + x)
nxL = 6ln + (5 * -1ln + x * -1ln)
nxL = 6ln + (-5ln + -1lnx)

Combine like terms: 6ln + -5ln = 1ln
nxL = 1ln + -1lnx

Solving
nxL = 1ln + -1lnx

Solving for variable 'n'.

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

Add '-1ln' to each side of the equation.
-1ln + nxL = 1ln + -1ln + -1lnx

Combine like terms: 1ln + -1ln = 0
-1ln + nxL = 0 + -1lnx
-1ln + nxL = -1lnx

Add 'lnx' to each side of the equation.
-1ln + lnx + nxL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-1ln + lnx + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1l + lx + 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 '(-1l + lx + xL)' equal to zero and attempt to solve:

Simplifying
-1l + lx + xL = 0

Solving
-1l + lx + xL = 0

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

Add 'l' to each side of the equation.
-1l + lx + l + xL = 0 + l

Reorder the terms:
-1l + l + lx + xL = 0 + l

Combine like terms: -1l + l = 0
0 + lx + xL = 0 + l
lx + xL = 0 + l
Remove the zero:
lx + xL = l

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

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

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

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

Simplifying
0 = l + -1lx + -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}