Ln(x)=ln(x-8)-ln(2)

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Solution for Ln(x)=ln(x-8)-ln(2) equation: 


Simplifying
Ln(x) = ln(x + -8) + -1ln(2)

Multiply nL * x
nxL = ln(x + -8) + -1ln(2)

Reorder the terms:
nxL = ln(-8 + x) + -1ln(2)
nxL = (-8 * ln + x * ln) + -1ln(2)
nxL = (-8ln + lnx) + -1ln(2)

Reorder the terms for easier multiplication:
nxL = -8ln + lnx + -1 * 2ln

Multiply -1 * 2
nxL = -8ln + lnx + -2ln

Reorder the terms:
nxL = -8ln + -2ln + lnx

Combine like terms: -8ln + -2ln = -10ln
nxL = -10ln + lnx

Solving
nxL = -10ln + lnx

Solving for variable 'n'.

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

Add '10ln' to each side of the equation.
10ln + nxL = -10ln + 10ln + lnx

Combine like terms: -10ln + 10ln = 0
10ln + nxL = 0 + lnx
10ln + nxL = lnx

Add '-1lnx' to each side of the equation.
10ln + -1lnx + nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
10ln + -1lnx + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(10l + -1lx + 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 '(10l + -1lx + xL)' equal to zero and attempt to solve:

Simplifying
10l + -1lx + xL = 0

Solving
10l + -1lx + xL = 0

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

Add '-10l' to each side of the equation.
10l + -1lx + -10l + xL = 0 + -10l

Reorder the terms:
10l + -10l + -1lx + xL = 0 + -10l

Combine like terms: 10l + -10l = 0
0 + -1lx + xL = 0 + -10l
-1lx + xL = 0 + -10l
Remove the zero:
-1lx + xL = -10l

Add 'lx' to each side of the equation.
-1lx + lx + xL = -10l + lx

Combine like terms: -1lx + lx = 0
0 + xL = -10l + lx
xL = -10l + lx

Add '-1xL' to each side of the equation.
xL + -1xL = -10l + lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -10l + lx + -1xL

Simplifying
0 = -10l + lx + -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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