ln(x+1)+ln(x-3)=ln(10)

Solution for ln(x+1)+ln(x-3)=ln(10) equation:

Simplifying
ln(x + 1) + ln(x + -3) = ln(10)

Reorder the terms:
ln(1 + x) + ln(x + -3) = ln(10)
(1 * ln + x * ln) + ln(x + -3) = ln(10)
(1ln + lnx) + ln(x + -3) = ln(10)

Reorder the terms:
1ln + lnx + ln(-3 + x) = ln(10)
1ln + lnx + (-3 * ln + x * ln) = ln(10)
1ln + lnx + (-3ln + lnx) = ln(10)

Reorder the terms:
1ln + -3ln + lnx + lnx = ln(10)

Combine like terms: 1ln + -3ln = -2ln
-2ln + lnx + lnx = ln(10)

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = ln(10)

Reorder the terms for easier multiplication:
-2ln + 2lnx = 10ln

Solving
-2ln + 2lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-2ln + -10ln + 2lnx = 10ln + -10ln

Combine like terms: -2ln + -10ln = -12ln
-12ln + 2lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 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.