ln(2x+13)-ln(x)=ln(3)

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Solution for ln(2x+13)-ln(x)=ln(3) equation: 


Simplifying
ln(2x + 13) + -1ln(x) = ln(3)

Reorder the terms:
ln(13 + 2x) + -1ln(x) = ln(3)
(13 * ln + 2x * ln) + -1ln(x) = ln(3)
(13ln + 2lnx) + -1ln(x) = ln(3)

Multiply ln * x
13ln + 2lnx + -1lnx = ln(3)

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

Reorder the terms for easier multiplication:
13ln + 1lnx = 3ln

Solving
13ln + 1lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
13ln + -3ln + 1lnx = 3ln + -3ln

Combine like terms: 13ln + -3ln = 10ln
10ln + 1lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
10ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Add '-1x' to each side of the equation.
x + -1x = -10 + -1x

Combine like terms: x + -1x = 0
0 = -10 + -1x

Simplifying
0 = -10 + -1x

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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