ln(2x+3)+ln(x-5)-2ln(x)=0

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Solution for ln(2x+3)+ln(x-5)-2ln(x)=0 equation: 


Simplifying
ln(2x + 3) + ln(x + -5) + -2ln(x) = 0

Reorder the terms:
ln(3 + 2x) + ln(x + -5) + -2ln(x) = 0
(3 * ln + 2x * ln) + ln(x + -5) + -2ln(x) = 0
(3ln + 2lnx) + ln(x + -5) + -2ln(x) = 0

Reorder the terms:
3ln + 2lnx + ln(-5 + x) + -2ln(x) = 0
3ln + 2lnx + (-5 * ln + x * ln) + -2ln(x) = 0
3ln + 2lnx + (-5ln + lnx) + -2ln(x) = 0

Multiply ln * x
3ln + 2lnx + -5ln + lnx + -2lnx = 0

Reorder the terms:
3ln + -5ln + 2lnx + lnx + -2lnx = 0

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

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

Combine like terms: 3lnx + -2lnx = 1lnx
-2ln + 1lnx = 0

Solving
-2ln + 1lnx = 0

Solving for variable 'l'.

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

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

Simplifying
-2 + x = 0

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

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

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

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

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

Simplifying
0 = 2 + -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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