ln(5x-4)=ln(2x^2-x)

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Solution for ln(5x-4)=ln(2x^2-x) equation: 


Simplifying
ln(5x + -4) = ln(2x2 + -1x)

Reorder the terms:
ln(-4 + 5x) = ln(2x2 + -1x)
(-4 * ln + 5x * ln) = ln(2x2 + -1x)
(-4ln + 5lnx) = ln(2x2 + -1x)

Reorder the terms:
-4ln + 5lnx = ln(-1x + 2x2)
-4ln + 5lnx = (-1x * ln + 2x2 * ln)
-4ln + 5lnx = (-1lnx + 2lnx2)

Solving
-4ln + 5lnx = -1lnx + 2lnx2

Solving for variable 'l'.

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

Add 'lnx' to each side of the equation.
-4ln + 5lnx + lnx = -1lnx + lnx + 2lnx2

Combine like terms: 5lnx + lnx = 6lnx
-4ln + 6lnx = -1lnx + lnx + 2lnx2

Combine like terms: -1lnx + lnx = 0
-4ln + 6lnx = 0 + 2lnx2
-4ln + 6lnx = 2lnx2

Add '-2lnx2' to each side of the equation.
-4ln + 6lnx + -2lnx2 = 2lnx2 + -2lnx2

Combine like terms: 2lnx2 + -2lnx2 = 0
-4ln + 6lnx + -2lnx2 = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-2 + 3x + -1x2) = 0

Factor a trinomial.
2ln((-2 + x)(1 + -1x)) = 0

Ignore the factor 2.

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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Add '-1x' to each side of the equation.
x + -1x = 2 + -1x

Combine like terms: x + -1x = 0
0 = 2 + -1x

Simplifying
0 = 2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing l 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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