In(x+2)=In(5x+1)

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Solution for In(x+2)=In(5x+1) equation: 


Simplifying
In(x + 2) = In(5x + 1)

Reorder the terms:
nI(2 + x) = In(5x + 1)
(2 * nI + x * nI) = In(5x + 1)
(2nI + nxI) = In(5x + 1)

Reorder the terms:
2nI + nxI = nI(1 + 5x)
2nI + nxI = (1 * nI + 5x * nI)
2nI + nxI = (1nI + 5nxI)

Solving
2nI + nxI = 1nI + 5nxI

Solving for variable 'n'.

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

Add '-1nI' to each side of the equation.
2nI + -1nI + nxI = 1nI + -1nI + 5nxI

Combine like terms: 2nI + -1nI = 1nI
1nI + nxI = 1nI + -1nI + 5nxI

Combine like terms: 1nI + -1nI = 0
1nI + nxI = 0 + 5nxI
1nI + nxI = 5nxI

Add '-5nxI' to each side of the equation.
1nI + nxI + -5nxI = 5nxI + -5nxI

Combine like terms: nxI + -5nxI = -4nxI
1nI + -4nxI = 5nxI + -5nxI

Combine like terms: 5nxI + -5nxI = 0
1nI + -4nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(1 + -4x) = 0


Subproblem 1
Set the factor 'nI' equal to zero and attempt to solve:

Simplifying
nI = 0

Solving
nI = 0

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

Simplifying
nI = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Add '4x' to each side of the equation.
-4x + 4x = -1 + 4x

Combine like terms: -4x + 4x = 0
0 = -1 + 4x

Simplifying
0 = -1 + 4x

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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