ln(2)*ln(x)+ln(x-2)=0

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Solution for ln(2)*ln(x)+ln(x-2)=0 equation: 


Simplifying
ln(2) * ln(x) + ln(x + -2) = 0

Reorder the terms for easier multiplication:
2ln * ln * x + ln(x + -2) = 0

Multiply ln * ln
2l2n2 * x + ln(x + -2) = 0

Multiply l2n2 * x
2l2n2x + ln(x + -2) = 0

Reorder the terms:
2l2n2x + ln(-2 + x) = 0
2l2n2x + (-2 * ln + x * ln) = 0
2l2n2x + (-2ln + lnx) = 0

Reorder the terms:
-2ln + lnx + 2l2n2x = 0

Solving
-2ln + lnx + 2l2n2x = 0

Solving for variable 'l'.

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

Simplifying
-2 + x + 2lnx = 0

Reorder the terms:
-2 + 2lnx + x = 0

Solving
-2 + 2lnx + 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 + 2lnx + 2 + x = 0 + 2

Reorder the terms:
-2 + 2 + 2lnx + x = 0 + 2

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

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

Add '-1x' to each side of the equation.
2lnx + x + -1x = 2 + -1x

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

Divide each side by '2nx'.
l = n-1x-1 + -0.5n-1

Simplifying
l = n-1x-1 + -0.5n-1

Reorder the terms:
l = -0.5n-1 + n-1x-1
Solution
l = {-0.5n-1 + n-1x-1}

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