ln(x+9)-ln(x-5)=lnx

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Solution for ln(x+9)-ln(x-5)=lnx equation: 


Simplifying
ln(x + 9) + -1ln(x + -5) = lnx

Reorder the terms:
ln(9 + x) + -1ln(x + -5) = lnx
(9 * ln + x * ln) + -1ln(x + -5) = lnx
(9ln + lnx) + -1ln(x + -5) = lnx

Reorder the terms:
9ln + lnx + -1ln(-5 + x) = lnx
9ln + lnx + (-5 * -1ln + x * -1ln) = lnx
9ln + lnx + (5ln + -1lnx) = lnx

Reorder the terms:
9ln + 5ln + lnx + -1lnx = lnx

Combine like terms: 9ln + 5ln = 14ln
14ln + lnx + -1lnx = lnx

Combine like terms: lnx + -1lnx = 0
14ln + 0 = lnx
14ln = lnx

Solving
14ln = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
14ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
14ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(14 + -1x) = 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 '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Add 'x' to each side of the equation.
-1x + x = -14 + x

Combine like terms: -1x + x = 0
0 = -14 + x

Simplifying
0 = -14 + x

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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