ln(4x-4)-ln(5x+1)=4

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Solution for ln(4x-4)-ln(5x+1)=4 equation: 


Simplifying
ln(4x + -4) + -1ln(5x + 1) = 4

Reorder the terms:
ln(-4 + 4x) + -1ln(5x + 1) = 4
(-4 * ln + 4x * ln) + -1ln(5x + 1) = 4
(-4ln + 4lnx) + -1ln(5x + 1) = 4

Reorder the terms:
-4ln + 4lnx + -1ln(1 + 5x) = 4
-4ln + 4lnx + (1 * -1ln + 5x * -1ln) = 4
-4ln + 4lnx + (-1ln + -5lnx) = 4

Reorder the terms:
-4ln + -1ln + 4lnx + -5lnx = 4

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

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

Solving
-5ln + -1lnx = 4

Solving for variable 'l'.

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

Reorder the terms:
-4 + -5ln + -1lnx = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -5ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 5ln + lnx) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + 5ln + lnx)' equal to zero and attempt to solve:

Simplifying
4 + 5ln + lnx = 0

Solving
4 + 5ln + lnx = 0

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

Add '-4' to each side of the equation.
4 + 5ln + -4 + lnx = 0 + -4

Reorder the terms:
4 + -4 + 5ln + lnx = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5ln + lnx = 0 + -4
5ln + lnx = 0 + -4

Combine like terms: 0 + -4 = -4
5ln + lnx = -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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