ln(8x+11)-lnx=ln(9)

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Solution for ln(8x+11)-lnx=ln(9) equation: 


Simplifying
ln(8x + 11) + -1lnx = ln(9)

Reorder the terms:
ln(11 + 8x) + -1lnx = ln(9)
(11 * ln + 8x * ln) + -1lnx = ln(9)
(11ln + 8lnx) + -1lnx = ln(9)

Combine like terms: 8lnx + -1lnx = 7lnx
11ln + 7lnx = ln(9)

Reorder the terms for easier multiplication:
11ln + 7lnx = 9ln

Solving
11ln + 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.
11ln + -9ln + 7lnx = 9ln + -9ln

Combine like terms: 11ln + -9ln = 2ln
2ln + 7lnx = 9ln + -9ln

Combine like terms: 9ln + -9ln = 0
2ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + 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 '(2 + 7x)' equal to zero and attempt to solve:

Simplifying
2 + 7x = 0

Solving
2 + 7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x = 0 + -2
7x = 0 + -2

Combine like terms: 0 + -2 = -2
7x = -2

Add '-7x' to each side of the equation.
7x + -7x = -2 + -7x

Combine like terms: 7x + -7x = 0
0 = -2 + -7x

Simplifying
0 = -2 + -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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