ln(x-3)=ln(x+17)-ln(x-1)

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Solution for ln(x-3)=ln(x+17)-ln(x-1) equation: 


Simplifying
ln(x + -3) = ln(x + 17) + -1ln(x + -1)

Reorder the terms:
ln(-3 + x) = ln(x + 17) + -1ln(x + -1)
(-3 * ln + x * ln) = ln(x + 17) + -1ln(x + -1)
(-3ln + lnx) = ln(x + 17) + -1ln(x + -1)

Reorder the terms:
-3ln + lnx = ln(17 + x) + -1ln(x + -1)
-3ln + lnx = (17 * ln + x * ln) + -1ln(x + -1)
-3ln + lnx = (17ln + lnx) + -1ln(x + -1)

Reorder the terms:
-3ln + lnx = 17ln + lnx + -1ln(-1 + x)
-3ln + lnx = 17ln + lnx + (-1 * -1ln + x * -1ln)
-3ln + lnx = 17ln + lnx + (1ln + -1lnx)

Reorder the terms:
-3ln + lnx = 17ln + 1ln + lnx + -1lnx

Combine like terms: 17ln + 1ln = 18ln
-3ln + lnx = 18ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-3ln + lnx = 18ln + 0
-3ln + lnx = 18ln

Solving
-3ln + 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.
-3ln + -18ln + lnx = 18ln + -18ln

Combine like terms: -3ln + -18ln = -21ln
-21ln + lnx = 18ln + -18ln

Combine like terms: 18ln + -18ln = 0
-21ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 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 '(-21 + x)' equal to zero and attempt to solve:

Simplifying
-21 + x = 0

Solving
-21 + x = 0

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

Add '21' to each side of the equation.
-21 + 21 + x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + x = 0 + 21
x = 0 + 21

Combine like terms: 0 + 21 = 21
x = 21

Add '-1x' to each side of the equation.
x + -1x = 21 + -1x

Combine like terms: x + -1x = 0
0 = 21 + -1x

Simplifying
0 = 21 + -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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