ln(3+x)+ln(2x-1)-2lnx=0

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Solution for ln(3+x)+ln(2x-1)-2lnx=0 equation: 


Simplifying
ln(3 + x) + ln(2x + -1) + -2lnx = 0
(3 * ln + x * ln) + ln(2x + -1) + -2lnx = 0
(3ln + lnx) + ln(2x + -1) + -2lnx = 0

Reorder the terms:
3ln + lnx + ln(-1 + 2x) + -2lnx = 0
3ln + lnx + (-1 * ln + 2x * ln) + -2lnx = 0
3ln + lnx + (-1ln + 2lnx) + -2lnx = 0

Reorder the terms:
3ln + -1ln + lnx + 2lnx + -2lnx = 0

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

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

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

Solving
2ln + 1lnx = 0

Solving for variable 'l'.

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

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

The solution to this equation could not be determined.

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