In(8-5x)=In(4x-1)

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Solution for In(8-5x)=In(4x-1) equation: 


Simplifying
In(8 + -5x) = In(4x + -1)
(8 * nI + -5x * nI) = In(4x + -1)
(8nI + -5nxI) = In(4x + -1)

Reorder the terms:
8nI + -5nxI = nI(-1 + 4x)
8nI + -5nxI = (-1 * nI + 4x * nI)
8nI + -5nxI = (-1nI + 4nxI)

Solving
8nI + -5nxI = -1nI + 4nxI

Solving for variable 'n'.

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

Add 'nI' to each side of the equation.
8nI + nI + -5nxI = -1nI + nI + 4nxI

Combine like terms: 8nI + nI = 9nI
9nI + -5nxI = -1nI + nI + 4nxI

Combine like terms: -1nI + nI = 0
9nI + -5nxI = 0 + 4nxI
9nI + -5nxI = 4nxI

Add '-4nxI' to each side of the equation.
9nI + -5nxI + -4nxI = 4nxI + -4nxI

Combine like terms: -5nxI + -4nxI = -9nxI
9nI + -9nxI = 4nxI + -4nxI

Combine like terms: 4nxI + -4nxI = 0
9nI + -9nxI = 0

Factor out the Greatest Common Factor (GCF), '9nI'.
9nI(1 + -1x) = 0

Ignore the factor 9.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

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

Simplifying
0 = -1 + 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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