ln(6x+9)=ln(4x-11)

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Solution for ln(6x+9)=ln(4x-11) equation: 


Simplifying
ln(6x + 9) = ln(4x + -11)

Reorder the terms:
ln(9 + 6x) = ln(4x + -11)
(9 * ln + 6x * ln) = ln(4x + -11)
(9ln + 6lnx) = ln(4x + -11)

Reorder the terms:
9ln + 6lnx = ln(-11 + 4x)
9ln + 6lnx = (-11 * ln + 4x * ln)
9ln + 6lnx = (-11ln + 4lnx)

Solving
9ln + 6lnx = -11ln + 4lnx

Solving for variable 'l'.

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

Add '11ln' to each side of the equation.
9ln + 11ln + 6lnx = -11ln + 11ln + 4lnx

Combine like terms: 9ln + 11ln = 20ln
20ln + 6lnx = -11ln + 11ln + 4lnx

Combine like terms: -11ln + 11ln = 0
20ln + 6lnx = 0 + 4lnx
20ln + 6lnx = 4lnx

Add '-4lnx' to each side of the equation.
20ln + 6lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 6lnx + -4lnx = 2lnx
20ln + 2lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
20ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(10 + x) = 0

Ignore the factor 2.

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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