In(3x+1)=In(2x-8)

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Solution for In(3x+1)=In(2x-8) equation: 


Simplifying
In(3x + 1) = In(2x + -8)

Reorder the terms:
nI(1 + 3x) = In(2x + -8)
(1 * nI + 3x * nI) = In(2x + -8)
(1nI + 3nxI) = In(2x + -8)

Reorder the terms:
1nI + 3nxI = nI(-8 + 2x)
1nI + 3nxI = (-8 * nI + 2x * nI)
1nI + 3nxI = (-8nI + 2nxI)

Solving
1nI + 3nxI = -8nI + 2nxI

Solving for variable 'n'.

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

Add '8nI' to each side of the equation.
1nI + 8nI + 3nxI = -8nI + 8nI + 2nxI

Combine like terms: 1nI + 8nI = 9nI
9nI + 3nxI = -8nI + 8nI + 2nxI

Combine like terms: -8nI + 8nI = 0
9nI + 3nxI = 0 + 2nxI
9nI + 3nxI = 2nxI

Add '-2nxI' to each side of the equation.
9nI + 3nxI + -2nxI = 2nxI + -2nxI

Combine like terms: 3nxI + -2nxI = 1nxI
9nI + 1nxI = 2nxI + -2nxI

Combine like terms: 2nxI + -2nxI = 0
9nI + 1nxI = 0

Factor out the Greatest Common Factor (GCF), 'nI'.
nI(9 + x) = 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 '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Add '-1x' to each side of the equation.
x + -1x = -9 + -1x

Combine like terms: x + -1x = 0
0 = -9 + -1x

Simplifying
0 = -9 + -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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