3ln(2x)=3+ln(27)

Solution for 3ln(2x)=3+ln(27) equation:

Simplifying
3ln(2x) = 3 + ln(27)

Remove parenthesis around (2x)
3ln * 2x = 3 + ln(27)

Reorder the terms for easier multiplication:
3 * 2ln * x = 3 + ln(27)

Multiply 3 * 2
6ln * x = 3 + ln(27)

Multiply ln * x
6lnx = 3 + ln(27)

Reorder the terms for easier multiplication:
6lnx = 3 + 27ln

Solving
6lnx = 3 + 27ln

Solving for variable 'l'.

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

Add '-27ln' to each side of the equation.
-27ln + 6lnx = 3 + 27ln + -27ln

Combine like terms: 27ln + -27ln = 0
-27ln + 6lnx = 3 + 0
-27ln + 6lnx = 3

Reorder the terms:
-3 + -27ln + 6lnx = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -27ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -9ln + 2lnx) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -9ln + 2lnx)' equal to zero and attempt to solve:

Simplifying
-1 + -9ln + 2lnx = 0

Solving
-1 + -9ln + 2lnx = 0

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

Add '1' to each side of the equation.
-1 + -9ln + 1 + 2lnx = 0 + 1

Reorder the terms:
-1 + 1 + -9ln + 2lnx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9ln + 2lnx = 0 + 1
-9ln + 2lnx = 0 + 1

Combine like terms: 0 + 1 = 1
-9ln + 2lnx = 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.