ln(x+9)=ln(x-4)-ln(x+4)

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Solution for ln(x+9)=ln(x-4)-ln(x+4) equation: 


Simplifying
ln(x + 9) = ln(x + -4) + -1ln(x + 4)

Reorder the terms:
ln(9 + x) = ln(x + -4) + -1ln(x + 4)
(9 * ln + x * ln) = ln(x + -4) + -1ln(x + 4)
(9ln + lnx) = ln(x + -4) + -1ln(x + 4)

Reorder the terms:
9ln + lnx = ln(-4 + x) + -1ln(x + 4)
9ln + lnx = (-4 * ln + x * ln) + -1ln(x + 4)
9ln + lnx = (-4ln + lnx) + -1ln(x + 4)

Reorder the terms:
9ln + lnx = -4ln + lnx + -1ln(4 + x)
9ln + lnx = -4ln + lnx + (4 * -1ln + x * -1ln)
9ln + lnx = -4ln + lnx + (-4ln + -1lnx)

Reorder the terms:
9ln + lnx = -4ln + -4ln + lnx + -1lnx

Combine like terms: -4ln + -4ln = -8ln
9ln + lnx = -8ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
9ln + lnx = -8ln + 0
9ln + lnx = -8ln

Solving
9ln + lnx = -8ln

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
9ln + 8ln + lnx = -8ln + 8ln

Combine like terms: 9ln + 8ln = 17ln
17ln + lnx = -8ln + 8ln

Combine like terms: -8ln + 8ln = 0
17ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(17 + 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 '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Add '-1x' to each side of the equation.
x + -1x = -17 + -1x

Combine like terms: x + -1x = 0
0 = -17 + -1x

Simplifying
0 = -17 + -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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