3ln(x)=5ln(1-x)

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Solution for 3ln(x)=5ln(1-x) equation: 


Simplifying
3ln(x) = 5ln(1 + -1x)

Multiply ln * x
3lnx = 5ln(1 + -1x)
3lnx = (1 * 5ln + -1x * 5ln)
3lnx = (5ln + -5lnx)

Solving
3lnx = 5ln + -5lnx

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
-5ln + 3lnx = 5ln + -5ln + -5lnx

Combine like terms: 5ln + -5ln = 0
-5ln + 3lnx = 0 + -5lnx
-5ln + 3lnx = -5lnx

Add '5lnx' to each side of the equation.
-5ln + 3lnx + 5lnx = -5lnx + 5lnx

Combine like terms: 3lnx + 5lnx = 8lnx
-5ln + 8lnx = -5lnx + 5lnx

Combine like terms: -5lnx + 5lnx = 0
-5ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 8x) = 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 '(-5 + 8x)' equal to zero and attempt to solve:

Simplifying
-5 + 8x = 0

Solving
-5 + 8x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 8x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 8x = 0 + 5
8x = 0 + 5

Combine like terms: 0 + 5 = 5
8x = 5

Add '-8x' to each side of the equation.
8x + -8x = 5 + -8x

Combine like terms: 8x + -8x = 0
0 = 5 + -8x

Simplifying
0 = 5 + -8x

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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