ln(8x+13)-ln(x)=ln(9)

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Solution for ln(8x+13)-ln(x)=ln(9) equation: 


Simplifying
ln(8x + 13) + -1ln(x) = ln(9)

Reorder the terms:
ln(13 + 8x) + -1ln(x) = ln(9)
(13 * ln + 8x * ln) + -1ln(x) = ln(9)
(13ln + 8lnx) + -1ln(x) = ln(9)

Multiply ln * x
13ln + 8lnx + -1lnx = ln(9)

Combine like terms: 8lnx + -1lnx = 7lnx
13ln + 7lnx = ln(9)

Reorder the terms for easier multiplication:
13ln + 7lnx = 9ln

Solving
13ln + 7lnx = 9ln

Solving for variable 'l'.

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

Add '-9ln' to each side of the equation.
13ln + -9ln + 7lnx = 9ln + -9ln

Combine like terms: 13ln + -9ln = 4ln
4ln + 7lnx = 9ln + -9ln

Combine like terms: 9ln + -9ln = 0
4ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(4 + 7x) = 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 '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Add '-7x' to each side of the equation.
7x + -7x = -4 + -7x

Combine like terms: 7x + -7x = 0
0 = -4 + -7x

Simplifying
0 = -4 + -7x

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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