ln(7x+13)-ln(x)=ln(8)

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Solution for ln(7x+13)-ln(x)=ln(8) equation: 


Simplifying
ln(7x + 13) + -1ln(x) = ln(8)

Reorder the terms:
ln(13 + 7x) + -1ln(x) = ln(8)
(13 * ln + 7x * ln) + -1ln(x) = ln(8)
(13ln + 7lnx) + -1ln(x) = ln(8)

Multiply ln * x
13ln + 7lnx + -1lnx = ln(8)

Combine like terms: 7lnx + -1lnx = 6lnx
13ln + 6lnx = ln(8)

Reorder the terms for easier multiplication:
13ln + 6lnx = 8ln

Solving
13ln + 6lnx = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
13ln + -8ln + 6lnx = 8ln + -8ln

Combine like terms: 13ln + -8ln = 5ln
5ln + 6lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
5ln + 6lnx = 0

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

Simplifying
5 + 6x = 0

Solving
5 + 6x = 0

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

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

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

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

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

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

Simplifying
0 = -5 + -6x

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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