ln(3x+1)+ln(x)=ln(2)

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Solution for ln(3x+1)+ln(x)=ln(2) equation: 


Simplifying
ln(3x + 1) + ln(x) = ln(2)

Reorder the terms:
ln(1 + 3x) + ln(x) = ln(2)
(1 * ln + 3x * ln) + ln(x) = ln(2)
(1ln + 3lnx) + ln(x) = ln(2)

Multiply ln * x
1ln + 3lnx + lnx = ln(2)

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

Reorder the terms for easier multiplication:
1ln + 4lnx = 2ln

Solving
1ln + 4lnx = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
1ln + -2ln + 4lnx = 2ln + -2ln

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 4x) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
-1 + 4x = 0

Solving
-1 + 4x = 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 + 4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x = 0 + 1
4x = 0 + 1

Combine like terms: 0 + 1 = 1
4x = 1

Add '-4x' to each side of the equation.
4x + -4x = 1 + -4x

Combine like terms: 4x + -4x = 0
0 = 1 + -4x

Simplifying
0 = 1 + -4x

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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