Lnx=ln(8+x)-ln(x+3)

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Solution for Lnx=ln(8+x)-ln(x+3) equation: 


Simplifying
Lnx = ln(8 + x) + -1ln(x + 3)
nxL = (8 * ln + x * ln) + -1ln(x + 3)
nxL = (8ln + lnx) + -1ln(x + 3)

Reorder the terms:
nxL = 8ln + lnx + -1ln(3 + x)
nxL = 8ln + lnx + (3 * -1ln + x * -1ln)
nxL = 8ln + lnx + (-3ln + -1lnx)

Reorder the terms:
nxL = 8ln + -3ln + lnx + -1lnx

Combine like terms: 8ln + -3ln = 5ln
nxL = 5ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
nxL = 5ln + 0
nxL = 5ln

Solving
nxL = 5ln

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.
-5ln + nxL = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-5ln + nxL = 0

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

Simplifying
-5l + xL = 0

Solving
-5l + 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 + xL = 0 + 5l

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

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

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

Simplifying
0 = 5l + -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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