ln(2x)=ln(3y)

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


Simplifying
ln(2x) = ln(3y)

Remove parenthesis around (2x)
ln * 2x = ln(3y)

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

Multiply ln * x
2lnx = ln(3y)

Remove parenthesis around (3y)
2lnx = ln * 3y

Reorder the terms for easier multiplication:
2lnx = 3ln * y

Multiply ln * y
2lnx = 3lny

Solving
2lnx = 3lny

Solving for variable 'l'.

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

Add '-3lny' to each side of the equation.
2lnx + -3lny = 3lny + -3lny

Combine like terms: 3lny + -3lny = 0
2lnx + -3lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2x + -3y) = 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 '(2x + -3y)' equal to zero and attempt to solve:

Simplifying
2x + -3y = 0

Solving
2x + -3y = 0

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

Add '-2x' to each side of the equation.
2x + -2x + -3y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -3y = 0 + -2x
-3y = 0 + -2x
Remove the zero:
-3y = -2x

Add '3y' to each side of the equation.
-3y + 3y = -2x + 3y

Combine like terms: -3y + 3y = 0
0 = -2x + 3y

Simplifying
0 = -2x + 3y

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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