ln(6x+13)-ln(x)=ln(7)

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Solution for ln(6x+13)-ln(x)=ln(7) equation: 


Simplifying
ln(6x + 13) + -1ln(x) = ln(7)

Reorder the terms:
ln(13 + 6x) + -1ln(x) = ln(7)
(13 * ln + 6x * ln) + -1ln(x) = ln(7)
(13ln + 6lnx) + -1ln(x) = ln(7)

Multiply ln * x
13ln + 6lnx + -1lnx = ln(7)

Combine like terms: 6lnx + -1lnx = 5lnx
13ln + 5lnx = ln(7)

Reorder the terms for easier multiplication:
13ln + 5lnx = 7ln

Solving
13ln + 5lnx = 7ln

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
13ln + -7ln + 5lnx = 7ln + -7ln

Combine like terms: 13ln + -7ln = 6ln
6ln + 5lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 0
6ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + 5x) = 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 '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Add '-5x' to each side of the equation.
5x + -5x = -6 + -5x

Combine like terms: 5x + -5x = 0
0 = -6 + -5x

Simplifying
0 = -6 + -5x

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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