ln(x-5)+ln(5x+1)=10

Solution for ln(x-5)+ln(5x+1)=10 equation:

Simplifying
ln(x + -5) + ln(5x + 1) = 10

Reorder the terms:
ln(-5 + x) + ln(5x + 1) = 10
(-5 * ln + x * ln) + ln(5x + 1) = 10
(-5ln + lnx) + ln(5x + 1) = 10

Reorder the terms:
-5ln + lnx + ln(1 + 5x) = 10
-5ln + lnx + (1 * ln + 5x * ln) = 10
-5ln + lnx + (1ln + 5lnx) = 10

Reorder the terms:
-5ln + 1ln + lnx + 5lnx = 10

Combine like terms: -5ln + 1ln = -4ln
-4ln + lnx + 5lnx = 10

Combine like terms: lnx + 5lnx = 6lnx
-4ln + 6lnx = 10

Solving
-4ln + 6lnx = 10

Solving for variable 'l'.

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

Reorder the terms:
-10 + -4ln + 6lnx = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -4ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -2ln + 3lnx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -2ln + 3lnx)' equal to zero and attempt to solve:

Simplifying
-5 + -2ln + 3lnx = 0

Solving
-5 + -2ln + 3lnx = 0

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

Add '5' to each side of the equation.
-5 + -2ln + 5 + 3lnx = 0 + 5

Reorder the terms:
-5 + 5 + -2ln + 3lnx = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2ln + 3lnx = 0 + 5
-2ln + 3lnx = 0 + 5

Combine like terms: 0 + 5 = 5
-2ln + 3lnx = 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.