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

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


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

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

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

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

Reorder the terms for easier multiplication:
3ln + 3lnx = 5ln

Solving
3ln + 3lnx = 5ln

Solving for variable 'l'.

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

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

Combine like terms: 3ln + -5ln = -2ln
-2ln + 3lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-2ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 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 '(-2 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 0

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

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

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

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

Combine like terms: 3x + -3x = 0
0 = 2 + -3x

Simplifying
0 = 2 + -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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