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

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


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

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

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

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

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

Combine like terms: 3lnx + -1lnx = 2lnx
-6ln + 2lnx = 0

Solving
-6ln + 2lnx = 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), '2ln'.
2ln(-3 + x) = 0

Ignore the factor 2.

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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

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

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

Simplifying
0 = 3 + -1x

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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