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

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


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

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

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

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

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

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

Reorder the terms for easier multiplication:
1ln + 5lnx = 5ln

Solving
1ln + 5lnx = 5ln

Solving for variable 'l'.

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

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

Combine like terms: 1ln + -5ln = -4ln
-4ln + 5lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-4ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + 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 '(-4 + 5x)' equal to zero and attempt to solve:

Simplifying
-4 + 5x = 0

Solving
-4 + 5x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5x = 0 + 4
5x = 0 + 4

Combine like terms: 0 + 4 = 4
5x = 4

Add '-5x' to each side of the equation.
5x + -5x = 4 + -5x

Combine like terms: 5x + -5x = 0
0 = 4 + -5x

Simplifying
0 = 4 + -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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