ln(x-3)+ln(x-2)=ln(x-7)

Solution for ln(x-3)+ln(x-2)=ln(x-7) equation:

Simplifying
ln(x + -3) + ln(x + -2) = ln(x + -7)

Reorder the terms:
ln(-3 + x) + ln(x + -2) = ln(x + -7)
(-3 * ln + x * ln) + ln(x + -2) = ln(x + -7)
(-3ln + lnx) + ln(x + -2) = ln(x + -7)

Reorder the terms:
-3ln + lnx + ln(-2 + x) = ln(x + -7)
-3ln + lnx + (-2 * ln + x * ln) = ln(x + -7)
-3ln + lnx + (-2ln + lnx) = ln(x + -7)

Reorder the terms:
-3ln + -2ln + lnx + lnx = ln(x + -7)

Combine like terms: -3ln + -2ln = -5ln
-5ln + lnx + lnx = ln(x + -7)

Combine like terms: lnx + lnx = 2lnx
-5ln + 2lnx = ln(x + -7)

Reorder the terms:
-5ln + 2lnx = ln(-7 + x)
-5ln + 2lnx = (-7 * ln + x * ln)
-5ln + 2lnx = (-7ln + lnx)

Solving
-5ln + 2lnx = -7ln + lnx

Solving for variable 'l'.

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

Add '7ln' to each side of the equation.
-5ln + 7ln + 2lnx = -7ln + 7ln + lnx

Combine like terms: -5ln + 7ln = 2ln
2ln + 2lnx = -7ln + 7ln + lnx

Combine like terms: -7ln + 7ln = 0
2ln + 2lnx = 0 + lnx
2ln + 2lnx = lnx

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

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

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

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.