Ln(6)=ln(x)-ln(8)

Solution for Ln(6)=ln(x)-ln(8) equation:

Simplifying
Ln(6) = ln(x) + -1ln(8)

Reorder the terms for easier multiplication:
6nL = ln(x) + -1ln(8)

Multiply ln * x
6nL = lnx + -1ln(8)

Reorder the terms for easier multiplication:
6nL = lnx + -1 * 8ln

Multiply -1 * 8
6nL = lnx + -8ln

Reorder the terms:
6nL = -8ln + lnx

Solving
6nL = -8ln + lnx

Solving for variable 'n'.

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

Add '8ln' to each side of the equation.
8ln + 6nL = -8ln + 8ln + lnx

Combine like terms: -8ln + 8ln = 0
8ln + 6nL = 0 + lnx
8ln + 6nL = lnx

Add '-1lnx' to each side of the equation.
8ln + -1lnx + 6nL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
8ln + -1lnx + 6nL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(8l + -1lx + 6L) = 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 '(8l + -1lx + 6L)' equal to zero and attempt to solve:

Simplifying
8l + -1lx + 6L = 0

Reorder the terms:
6L + 8l + -1lx = 0

Solving
6L + 8l + -1lx = 0

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

Add '-6L' to each side of the equation.
6L + 8l + -6L + -1lx = 0 + -6L

Reorder the terms:
6L + -6L + 8l + -1lx = 0 + -6L

Combine like terms: 6L + -6L = 0
0 + 8l + -1lx = 0 + -6L
8l + -1lx = 0 + -6L
Remove the zero:
8l + -1lx = -6L

Add '-8l' to each side of the equation.
8l + -8l + -1lx = -6L + -8l

Combine like terms: 8l + -8l = 0
0 + -1lx = -6L + -8l
-1lx = -6L + -8l

Add 'lx' to each side of the equation.
-1lx + lx = -6L + -8l + lx

Combine like terms: -1lx + lx = 0
0 = -6L + -8l + lx

Simplifying
0 = -6L + -8l + lx

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}