ln(x)+ln(2-x)=3lnx

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Solution for ln(x)+ln(2-x)=3lnx equation: 


Simplifying
ln(x) + ln(2 + -1x) = 3lnx

Multiply ln * x
lnx + ln(2 + -1x) = 3lnx
lnx + (2 * ln + -1x * ln) = 3lnx
lnx + (2ln + -1lnx) = 3lnx

Reorder the terms:
2ln + lnx + -1lnx = 3lnx

Combine like terms: lnx + -1lnx = 0
2ln + 0 = 3lnx
2ln = 3lnx

Solving
2ln = 3lnx

Solving for variable 'l'.

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

Add '-3lnx' to each side of the equation.
2ln + -3lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
2ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -3x) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Add '3x' to each side of the equation.
-3x + 3x = -2 + 3x

Combine like terms: -3x + 3x = 0
0 = -2 + 3x

Simplifying
0 = -2 + 3x

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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