ln(x+8)=ln(x-9)-ln(x+9)

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Solution for ln(x+8)=ln(x-9)-ln(x+9) equation: 


Simplifying
ln(x + 8) = ln(x + -9) + -1ln(x + 9)

Reorder the terms:
ln(8 + x) = ln(x + -9) + -1ln(x + 9)
(8 * ln + x * ln) = ln(x + -9) + -1ln(x + 9)
(8ln + lnx) = ln(x + -9) + -1ln(x + 9)

Reorder the terms:
8ln + lnx = ln(-9 + x) + -1ln(x + 9)
8ln + lnx = (-9 * ln + x * ln) + -1ln(x + 9)
8ln + lnx = (-9ln + lnx) + -1ln(x + 9)

Reorder the terms:
8ln + lnx = -9ln + lnx + -1ln(9 + x)
8ln + lnx = -9ln + lnx + (9 * -1ln + x * -1ln)
8ln + lnx = -9ln + lnx + (-9ln + -1lnx)

Reorder the terms:
8ln + lnx = -9ln + -9ln + lnx + -1lnx

Combine like terms: -9ln + -9ln = -18ln
8ln + lnx = -18ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
8ln + lnx = -18ln + 0
8ln + lnx = -18ln

Solving
8ln + lnx = -18ln

Solving for variable 'l'.

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

Add '18ln' to each side of the equation.
8ln + 18ln + lnx = -18ln + 18ln

Combine like terms: 8ln + 18ln = 26ln
26ln + lnx = -18ln + 18ln

Combine like terms: -18ln + 18ln = 0
26ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(26 + 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 '(26 + x)' equal to zero and attempt to solve:

Simplifying
26 + x = 0

Solving
26 + x = 0

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

Add '-26' to each side of the equation.
26 + -26 + x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + x = 0 + -26
x = 0 + -26

Combine like terms: 0 + -26 = -26
x = -26

Add '-1x' to each side of the equation.
x + -1x = -26 + -1x

Combine like terms: x + -1x = 0
0 = -26 + -1x

Simplifying
0 = -26 + -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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