ln(5x+1)+lnx-ln(3x+2)=0

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Solution for ln(5x+1)+lnx-ln(3x+2)=0 equation: 


Simplifying
ln(5x + 1) + lnx + -1ln(3x + 2) = 0

Reorder the terms:
ln(1 + 5x) + lnx + -1ln(3x + 2) = 0
(1 * ln + 5x * ln) + lnx + -1ln(3x + 2) = 0
(1ln + 5lnx) + lnx + -1ln(3x + 2) = 0

Reorder the terms:
1ln + 5lnx + lnx + -1ln(2 + 3x) = 0
1ln + 5lnx + lnx + (2 * -1ln + 3x * -1ln) = 0
1ln + 5lnx + lnx + (-2ln + -3lnx) = 0

Reorder the terms:
1ln + -2ln + 5lnx + lnx + -3lnx = 0

Combine like terms: 1ln + -2ln = -1ln
-1ln + 5lnx + lnx + -3lnx = 0

Combine like terms: 5lnx + lnx = 6lnx
-1ln + 6lnx + -3lnx = 0

Combine like terms: 6lnx + -3lnx = 3lnx
-1ln + 3lnx = 0

Solving
-1ln + 3lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 3x) = 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 '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

Add '-3x' to each side of the equation.
3x + -3x = 1 + -3x

Combine like terms: 3x + -3x = 0
0 = 1 + -3x

Simplifying
0 = 1 + -3x

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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