ln(5x-2)+ln(4x)=2lnx

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


Simplifying
ln(5x + -2) + ln(4x) = 2lnx

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

Remove parenthesis around (4x)
-2ln + 5lnx + ln * 4x = 2lnx

Reorder the terms for easier multiplication:
-2ln + 5lnx + 4ln * x = 2lnx

Multiply ln * x
-2ln + 5lnx + 4lnx = 2lnx

Combine like terms: 5lnx + 4lnx = 9lnx
-2ln + 9lnx = 2lnx

Solving
-2ln + 9lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
-2ln + 9lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 9lnx + -2lnx = 7lnx
-2ln + 7lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-2ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 7x) = 0


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 + 7x)' equal to zero and attempt to solve:

Simplifying
-2 + 7x = 0

Solving
-2 + 7x = 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 + 7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7x = 0 + 2
7x = 0 + 2

Combine like terms: 0 + 2 = 2
7x = 2

Add '-7x' to each side of the equation.
7x + -7x = 2 + -7x

Combine like terms: 7x + -7x = 0
0 = 2 + -7x

Simplifying
0 = 2 + -7x

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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