ln(5x-4)=log(-9x+8)

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Solution for ln(5x-4)=log(-9x+8) equation: 


Simplifying
ln(5x + -4) = log(-9x + 8)

Reorder the terms:
ln(-4 + 5x) = log(-9x + 8)
(-4 * ln + 5x * ln) = log(-9x + 8)
(-4ln + 5lnx) = log(-9x + 8)

Reorder the terms:
-4ln + 5lnx = glo(8 + -9x)
-4ln + 5lnx = (8 * glo + -9x * glo)
-4ln + 5lnx = (8glo + -9glox)

Solving
-4ln + 5lnx = 8glo + -9glox

Solving for variable 'l'.

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

Add '-8glo' to each side of the equation.
-4ln + -8glo + 5lnx = 8glo + -8glo + -9glox

Reorder the terms:
-8glo + -4ln + 5lnx = 8glo + -8glo + -9glox

Combine like terms: 8glo + -8glo = 0
-8glo + -4ln + 5lnx = 0 + -9glox
-8glo + -4ln + 5lnx = -9glox

Add '9glox' to each side of the equation.
-8glo + -4ln + 9glox + 5lnx = -9glox + 9glox

Reorder the terms:
-8glo + 9glox + -4ln + 5lnx = -9glox + 9glox

Combine like terms: -9glox + 9glox = 0
-8glo + 9glox + -4ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'l'.
l(-8go + 9gox + -4n + 5nx) = 0


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

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0

Subproblem 2
Set the factor '(-8go + 9gox + -4n + 5nx)' equal to zero and attempt to solve:

Simplifying
-8go + 9gox + -4n + 5nx = 0

Solving
-8go + 9gox + -4n + 5nx = 0

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

Add '8go' to each side of the equation.
-8go + 9gox + -4n + 8go + 5nx = 0 + 8go

Reorder the terms:
-8go + 8go + 9gox + -4n + 5nx = 0 + 8go

Combine like terms: -8go + 8go = 0
0 + 9gox + -4n + 5nx = 0 + 8go
9gox + -4n + 5nx = 0 + 8go
Remove the zero:
9gox + -4n + 5nx = 8go

Add '-9gox' to each side of the equation.
9gox + -4n + -9gox + 5nx = 8go + -9gox

Reorder the terms:
9gox + -9gox + -4n + 5nx = 8go + -9gox

Combine like terms: 9gox + -9gox = 0
0 + -4n + 5nx = 8go + -9gox
-4n + 5nx = 8go + -9gox

Add '4n' to each side of the equation.
-4n + 4n + 5nx = 8go + -9gox + 4n

Combine like terms: -4n + 4n = 0
0 + 5nx = 8go + -9gox + 4n
5nx = 8go + -9gox + 4n

Add '-5nx' to each side of the equation.
5nx + -5nx = 8go + -9gox + 4n + -5nx

Combine like terms: 5nx + -5nx = 0
0 = 8go + -9gox + 4n + -5nx

Simplifying
0 = 8go + -9gox + 4n + -5nx

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
l = {0}

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