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

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


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

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

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

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = ln(3)

Reorder the terms for easier multiplication:
-2ln + 2lnx = 3ln

Solving
-2ln + 2lnx = 3ln

Solving for variable 'l'.

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

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

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

Combine like terms: 3ln + -3ln = 0
-5ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 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 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Add '-2x' to each side of the equation.
2x + -2x = 5 + -2x

Combine like terms: 2x + -2x = 0
0 = 5 + -2x

Simplifying
0 = 5 + -2x

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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