ln(3x-6)=3+ln(3)

Solution for ln(3x-6)=3+ln(3) equation:

Simplifying
ln(3x + -6) = 3 + ln(3)

Reorder the terms:
ln(-6 + 3x) = 3 + ln(3)
(-6 * ln + 3x * ln) = 3 + ln(3)
(-6ln + 3lnx) = 3 + ln(3)

Reorder the terms for easier multiplication:
-6ln + 3lnx = 3 + 3ln

Solving
-6ln + 3lnx = 3 + 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-6ln + -3ln + 3lnx = 3 + 3ln + -3ln

Combine like terms: -6ln + -3ln = -9ln
-9ln + 3lnx = 3 + 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-9ln + 3lnx = 3 + 0
-9ln + 3lnx = 3

Reorder the terms:
-3 + -9ln + 3lnx = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -9ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -3ln + lnx) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -3ln + lnx)' equal to zero and attempt to solve:

Simplifying
-1 + -3ln + lnx = 0

Solving
-1 + -3ln + lnx = 0

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

Add '1' to each side of the equation.
-1 + -3ln + 1 + lnx = 0 + 1

Reorder the terms:
-1 + 1 + -3ln + lnx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3ln + lnx = 0 + 1
-3ln + lnx = 0 + 1

Combine like terms: 0 + 1 = 1
-3ln + lnx = 1

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.