ln(7x-4)+ln(6x)=2lnx

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Solution for ln(7x-4)+ln(6x)=2lnx equation: 


Simplifying
ln(7x + -4) + ln(6x) = 2lnx

Reorder the terms:
ln(-4 + 7x) + ln(6x) = 2lnx
(-4 * ln + 7x * ln) + ln(6x) = 2lnx
(-4ln + 7lnx) + ln(6x) = 2lnx

Remove parenthesis around (6x)
-4ln + 7lnx + ln * 6x = 2lnx

Reorder the terms for easier multiplication:
-4ln + 7lnx + 6ln * x = 2lnx

Multiply ln * x
-4ln + 7lnx + 6lnx = 2lnx

Combine like terms: 7lnx + 6lnx = 13lnx
-4ln + 13lnx = 2lnx

Solving
-4ln + 13lnx = 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.
-4ln + 13lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 13lnx + -2lnx = 11lnx
-4ln + 11lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-4ln + 11lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + 11x) = 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 '(-4 + 11x)' equal to zero and attempt to solve:

Simplifying
-4 + 11x = 0

Solving
-4 + 11x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 11x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 11x = 0 + 4
11x = 0 + 4

Combine like terms: 0 + 4 = 4
11x = 4

Add '-11x' to each side of the equation.
11x + -11x = 4 + -11x

Combine like terms: 11x + -11x = 0
0 = 4 + -11x

Simplifying
0 = 4 + -11x

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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