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

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

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

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

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

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

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

Combine like terms: lnx + 3lnx = 4lnx
-2ln + 4lnx = 10

Solving
-2ln + 4lnx = 10

Solving for variable 'l'.

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

Reorder the terms:
-10 + -2ln + 4lnx = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -2ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1ln + 2lnx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1ln + 2lnx)' equal to zero and attempt to solve:

Simplifying
-5 + -1ln + 2lnx = 0

Solving
-5 + -1ln + 2lnx = 0

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

Add '5' to each side of the equation.
-5 + -1ln + 5 + 2lnx = 0 + 5

Reorder the terms:
-5 + 5 + -1ln + 2lnx = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1ln + 2lnx = 0 + 5
-1ln + 2lnx = 0 + 5

Combine like terms: 0 + 5 = 5
-1ln + 2lnx = 5

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.