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

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


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

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

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

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

Combine like terms: -3ln + -2ln = -5ln
-5ln + 2lnx + lnx = 2lnx

Combine like terms: 2lnx + lnx = 3lnx
-5ln + 3lnx = 2lnx

Solving
-5ln + 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.
-5ln + 3lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 3lnx + -2lnx = 1lnx
-5ln + 1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-5ln + 1lnx = 0

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Add '-1x' to each side of the equation.
x + -1x = 5 + -1x

Combine like terms: x + -1x = 0
0 = 5 + -1x

Simplifying
0 = 5 + -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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