ln(3x+13)-ln(x)=ln(4)

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Solution for ln(3x+13)-ln(x)=ln(4) equation: 


Simplifying
ln(3x + 13) + -1ln(x) = ln(4)

Reorder the terms:
ln(13 + 3x) + -1ln(x) = ln(4)
(13 * ln + 3x * ln) + -1ln(x) = ln(4)
(13ln + 3lnx) + -1ln(x) = ln(4)

Multiply ln * x
13ln + 3lnx + -1lnx = ln(4)

Combine like terms: 3lnx + -1lnx = 2lnx
13ln + 2lnx = ln(4)

Reorder the terms for easier multiplication:
13ln + 2lnx = 4ln

Solving
13ln + 2lnx = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
13ln + -4ln + 2lnx = 4ln + -4ln

Combine like terms: 13ln + -4ln = 9ln
9ln + 2lnx = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
9ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(9 + 2x) = 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 '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Add '-2x' to each side of the equation.
2x + -2x = -9 + -2x

Combine like terms: 2x + -2x = 0
0 = -9 + -2x

Simplifying
0 = -9 + -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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