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

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


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

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

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

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

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

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

Solving
-1ln + 3lnx = 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.
-1ln + 3lnx + -2lnx = 2lnx + -2lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Add '-1x' to each side of the equation.
x + -1x = 1 + -1x

Combine like terms: x + -1x = 0
0 = 1 + -1x

Simplifying
0 = 1 + -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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