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

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


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

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

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

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

Combine like terms: -5ln + 1ln = -4ln
(-4ln + lnx + 5lnx) = 6

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

Remove parenthesis around (-4ln + 6lnx)
-4ln + 6lnx = 6

Solving
-4ln + 6lnx = 6

Solving for variable 'l'.

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

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

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

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

Ignore the factor 2.

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

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

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

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

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

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

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

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

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.

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