ln(x-1)+ln(x-6)=ln(5)

Solution for ln(x-1)+ln(x-6)=ln(5) equation:

Simplifying
ln(x + -1) + ln(x + -6) = ln(5)

Reorder the terms:
ln(-1 + x) + ln(x + -6) = ln(5)
(-1 * ln + x * ln) + ln(x + -6) = ln(5)
(-1ln + lnx) + ln(x + -6) = ln(5)

Reorder the terms:
-1ln + lnx + ln(-6 + x) = ln(5)
-1ln + lnx + (-6 * ln + x * ln) = ln(5)
-1ln + lnx + (-6ln + lnx) = ln(5)

Reorder the terms:
-1ln + -6ln + lnx + lnx = ln(5)

Combine like terms: -1ln + -6ln = -7ln
-7ln + lnx + lnx = ln(5)

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

Reorder the terms for easier multiplication:
-7ln + 2lnx = 5ln

Solving
-7ln + 2lnx = 5ln

Solving for variable 'l'.

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

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

Combine like terms: -7ln + -5ln = -12ln
-12ln + 2lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-12ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-6 + x) = 0

Ignore the factor 2.
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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Add '-1x' to each side of the equation.
x + -1x = 6 + -1x

Combine like terms: x + -1x = 0
0 = 6 + -1x

Simplifying
0 = 6 + -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.