2ln(3x)-ln(2)=ln(x)

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Solution for 2ln(3x)-ln(2)=ln(x) equation: 


Simplifying
2ln(3x) + -1ln(2) = ln(x)

Remove parenthesis around (3x)
2ln * 3x + -1ln(2) = ln(x)

Reorder the terms for easier multiplication:
2 * 3ln * x + -1ln(2) = ln(x)

Multiply 2 * 3
6ln * x + -1ln(2) = ln(x)

Multiply ln * x
6lnx + -1ln(2) = ln(x)

Reorder the terms for easier multiplication:
6lnx + -1 * 2ln = ln(x)

Multiply -1 * 2
6lnx + -2ln = ln(x)

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

Multiply ln * x
-2ln + 6lnx = lnx

Solving
-2ln + 6lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-2ln + 6lnx + -1lnx = lnx + -1lnx

Combine like terms: 6lnx + -1lnx = 5lnx
-2ln + 5lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-2ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 5x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-2 + 5x)' equal to zero and attempt to solve:

Simplifying
-2 + 5x = 0

Solving
-2 + 5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x = 0 + 2
5x = 0 + 2

Combine like terms: 0 + 2 = 2
5x = 2

Add '-5x' to each side of the equation.
5x + -5x = 2 + -5x

Combine like terms: 5x + -5x = 0
0 = 2 + -5x

Simplifying
0 = 2 + -5x

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.

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