42=6ln(x-2)

Solution for 42=6ln(x-2) equation:

Simplifying
42 = 6ln(x + -2)

Reorder the terms:
42 = 6ln(-2 + x)
42 = (-2 * 6ln + x * 6ln)
42 = (-12ln + 6lnx)

Solving
42 = -12ln + 6lnx

Solving for variable 'l'.

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

Add '12ln' to each side of the equation.
42 + 12ln = -12ln + 12ln + 6lnx

Combine like terms: -12ln + 12ln = 0
42 + 12ln = 0 + 6lnx
42 + 12ln = 6lnx

Add '-6lnx' to each side of the equation.
42 + 12ln + -6lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
42 + 12ln + -6lnx = 0

Add '-42' to each side of the equation.
42 + 12ln + -42 + -6lnx = 0 + -42

Reorder the terms:
42 + -42 + 12ln + -6lnx = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 12ln + -6lnx = 0 + -42
12ln + -6lnx = 0 + -42

Combine like terms: 0 + -42 = -42
12ln + -6lnx = -42

Reorder the terms:
42 + 12ln + -6lnx = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 12ln + -6lnx = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 2ln + -1lnx) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + 2ln + -1lnx)' equal to zero and attempt to solve:

Simplifying
7 + 2ln + -1lnx = 0

Solving
7 + 2ln + -1lnx = 0

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

Add '-7' to each side of the equation.
7 + 2ln + -7 + -1lnx = 0 + -7

Reorder the terms:
7 + -7 + 2ln + -1lnx = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2ln + -1lnx = 0 + -7
2ln + -1lnx = 0 + -7

Combine like terms: 0 + -7 = -7
2ln + -1lnx = -7

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.