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

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Solution for ln(4x+1)-ln(3)= equation: 


Simplifying
ln(4x + 1) + -1ln(3) = 0

Reorder the terms:
ln(1 + 4x) + -1ln(3) = 0
(1 * ln + 4x * ln) + -1ln(3) = 0
(1ln + 4lnx) + -1ln(3) = 0

Reorder the terms for easier multiplication:
1ln + 4lnx + -1 * 3ln = 0

Multiply -1 * 3
1ln + 4lnx + -3ln = 0

Reorder the terms:
1ln + -3ln + 4lnx = 0

Combine like terms: 1ln + -3ln = -2ln
-2ln + 4lnx = 0

Solving
-2ln + 4lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-1 + 2x) = 0

Ignore the factor 2.

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 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Add '-2x' to each side of the equation.
2x + -2x = 1 + -2x

Combine like terms: 2x + -2x = 0
0 = 1 + -2x

Simplifying
0 = 1 + -2x

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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