ln(5x+1)=ln(6x-2)

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Solution for ln(5x+1)=ln(6x-2) equation: 


Simplifying
ln(5x + 1) = ln(6x + -2)

Reorder the terms:
ln(1 + 5x) = ln(6x + -2)
(1 * ln + 5x * ln) = ln(6x + -2)
(1ln + 5lnx) = ln(6x + -2)

Reorder the terms:
1ln + 5lnx = ln(-2 + 6x)
1ln + 5lnx = (-2 * ln + 6x * ln)
1ln + 5lnx = (-2ln + 6lnx)

Solving
1ln + 5lnx = -2ln + 6lnx

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
1ln + 2ln + 5lnx = -2ln + 2ln + 6lnx

Combine like terms: 1ln + 2ln = 3ln
3ln + 5lnx = -2ln + 2ln + 6lnx

Combine like terms: -2ln + 2ln = 0
3ln + 5lnx = 0 + 6lnx
3ln + 5lnx = 6lnx

Add '-6lnx' to each side of the equation.
3ln + 5lnx + -6lnx = 6lnx + -6lnx

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

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

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

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

Simplifying
0 = -3 + x

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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