ln(x-5)+ln(5x+1)=8

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Solution for ln(x-5)+ln(5x+1)=8 equation:


Simplifying
ln(x + -5) + ln(5x + 1) = 8

Reorder the terms:
ln(-5 + x) + ln(5x + 1) = 8
(-5 * ln + x * ln) + ln(5x + 1) = 8
(-5ln + lnx) + ln(5x + 1) = 8

Reorder the terms:
-5ln + lnx + ln(1 + 5x) = 8
-5ln + lnx + (1 * ln + 5x * ln) = 8
-5ln + lnx + (1ln + 5lnx) = 8

Reorder the terms:
-5ln + 1ln + lnx + 5lnx = 8

Combine like terms: -5ln + 1ln = -4ln
-4ln + lnx + 5lnx = 8

Combine like terms: lnx + 5lnx = 6lnx
-4ln + 6lnx = 8

Solving
-4ln + 6lnx = 8

Solving for variable 'l'.

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

Reorder the terms:
-8 + -4ln + 6lnx = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -4ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -2ln + 3lnx) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -2ln + 3lnx)' equal to zero and attempt to solve: Simplifying -4 + -2ln + 3lnx = 0 Solving -4 + -2ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + -2ln + 4 + 3lnx = 0 + 4 Reorder the terms: -4 + 4 + -2ln + 3lnx = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2ln + 3lnx = 0 + 4 -2ln + 3lnx = 0 + 4 Combine like terms: 0 + 4 = 4 -2ln + 3lnx = 4 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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