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

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


Simplifying
ln(5 + 4x) + -1ln(3 + x) = ln(3)
(5 * ln + 4x * ln) + -1ln(3 + x) = ln(3)
(5ln + 4lnx) + -1ln(3 + x) = ln(3)
5ln + 4lnx + (3 * -1ln + x * -1ln) = ln(3)
5ln + 4lnx + (-3ln + -1lnx) = ln(3)

Reorder the terms:
5ln + -3ln + 4lnx + -1lnx = ln(3)

Combine like terms: 5ln + -3ln = 2ln
2ln + 4lnx + -1lnx = ln(3)

Combine like terms: 4lnx + -1lnx = 3lnx
2ln + 3lnx = ln(3)

Reorder the terms for easier multiplication:
2ln + 3lnx = 3ln

Solving
2ln + 3lnx = 3ln

Solving for variable 'l'.

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

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

Combine like terms: 2ln + -3ln = -1ln
-1ln + 3lnx = 3ln + -3ln

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 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 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

Add '-3x' to each side of the equation.
3x + -3x = 1 + -3x

Combine like terms: 3x + -3x = 0
0 = 1 + -3x

Simplifying
0 = 1 + -3x

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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