ln(3x+5)=ln(4-5x)

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Solution for ln(3x+5)=ln(4-5x) equation: 


Simplifying
ln(3x + 5) = ln(4 + -5x)

Reorder the terms:
ln(5 + 3x) = ln(4 + -5x)
(5 * ln + 3x * ln) = ln(4 + -5x)
(5ln + 3lnx) = ln(4 + -5x)
5ln + 3lnx = (4 * ln + -5x * ln)
5ln + 3lnx = (4ln + -5lnx)

Solving
5ln + 3lnx = 4ln + -5lnx

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
5ln + -4ln + 3lnx = 4ln + -4ln + -5lnx

Combine like terms: 5ln + -4ln = 1ln
1ln + 3lnx = 4ln + -4ln + -5lnx

Combine like terms: 4ln + -4ln = 0
1ln + 3lnx = 0 + -5lnx
1ln + 3lnx = -5lnx

Add '5lnx' to each side of the equation.
1ln + 3lnx + 5lnx = -5lnx + 5lnx

Combine like terms: 3lnx + 5lnx = 8lnx
1ln + 8lnx = -5lnx + 5lnx

Combine like terms: -5lnx + 5lnx = 0
1ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 8x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8x = 0 + -1
8x = 0 + -1

Combine like terms: 0 + -1 = -1
8x = -1

Add '-8x' to each side of the equation.
8x + -8x = -1 + -8x

Combine like terms: 8x + -8x = 0
0 = -1 + -8x

Simplifying
0 = -1 + -8x

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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