ln(x)+ln(x-2)-ln(2)-ln(x)=ln(5)

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Solution for ln(x)+ln(x-2)-ln(2)-ln(x)=ln(5) equation: 


Simplifying
ln(x) + ln(x + -2) + -1ln(2) + -1ln(x) = ln(5)

Multiply ln * x
lnx + ln(x + -2) + -1ln(2) + -1ln(x) = ln(5)

Reorder the terms:
lnx + ln(-2 + x) + -1ln(2) + -1ln(x) = ln(5)
lnx + (-2 * ln + x * ln) + -1ln(2) + -1ln(x) = ln(5)
lnx + (-2ln + lnx) + -1ln(2) + -1ln(x) = ln(5)

Reorder the terms for easier multiplication:
lnx + -2ln + lnx + -1 * 2ln + -1ln(x) = ln(5)

Multiply -1 * 2
lnx + -2ln + lnx + -2ln + -1ln(x) = ln(5)

Multiply ln * x
lnx + -2ln + lnx + -2ln + -1lnx = ln(5)

Reorder the terms:
-2ln + -2ln + lnx + lnx + -1lnx = ln(5)

Combine like terms: -2ln + -2ln = -4ln
-4ln + lnx + lnx + -1lnx = ln(5)

Combine like terms: lnx + lnx = 2lnx
-4ln + 2lnx + -1lnx = ln(5)

Combine like terms: 2lnx + -1lnx = 1lnx
-4ln + 1lnx = ln(5)

Reorder the terms for easier multiplication:
-4ln + 1lnx = 5ln

Solving
-4ln + 1lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
-4ln + -5ln + 1lnx = 5ln + -5ln

Combine like terms: -4ln + -5ln = -9ln
-9ln + 1lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-9ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Add '-1x' to each side of the equation.
x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
0 = 9 + -1x

Simplifying
0 = 9 + -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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