-2lnx=ln(x-5)

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


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

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

Solving
-2lnx = -5ln + lnx

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

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

Add '-1lnx' to each side of the equation.
5ln + -2lnx + -1lnx = lnx + -1lnx

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

Combine like terms: lnx + -1lnx = 0
5ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -3x) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Add '3x' to each side of the equation.
-3x + 3x = -5 + 3x

Combine like terms: -3x + 3x = 0
0 = -5 + 3x

Simplifying
0 = -5 + 3x

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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