ln(3x+1)=ln(6x)

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Solution for ln(3x+1)=ln(6x) equation: 


Simplifying
ln(3x + 1) = ln(6x)

Reorder the terms:
ln(1 + 3x) = ln(6x)
(1 * ln + 3x * ln) = ln(6x)
(1ln + 3lnx) = ln(6x)

Remove parenthesis around (6x)
1ln + 3lnx = ln * 6x

Reorder the terms for easier multiplication:
1ln + 3lnx = 6ln * x

Multiply ln * x
1ln + 3lnx = 6lnx

Solving
1ln + 3lnx = 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
1ln + 3lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 3lnx + -6lnx = -3lnx
1ln + -3lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 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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