ln(9x+4)=ln(6x-5)

Solution for ln(9x+4)=ln(6x-5) equation:

Simplifying
ln(9x + 4) = ln(6x + -5)

Reorder the terms:
ln(4 + 9x) = ln(6x + -5)
(4 * ln + 9x * ln) = ln(6x + -5)
(4ln + 9lnx) = ln(6x + -5)

Reorder the terms:
4ln + 9lnx = ln(-5 + 6x)
4ln + 9lnx = (-5 * ln + 6x * ln)
4ln + 9lnx = (-5ln + 6lnx)

Solving
4ln + 9lnx = -5ln + 6lnx

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
4ln + 5ln + 9lnx = -5ln + 5ln + 6lnx

Combine like terms: 4ln + 5ln = 9ln
9ln + 9lnx = -5ln + 5ln + 6lnx

Combine like terms: -5ln + 5ln = 0
9ln + 9lnx = 0 + 6lnx
9ln + 9lnx = 6lnx

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

Combine like terms: 9lnx + -6lnx = 3lnx
9ln + 3lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
9ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(3 + x) = 0

Ignore the factor 3.
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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Add '-1x' to each side of the equation.
x + -1x = -3 + -1x

Combine like terms: x + -1x = 0
0 = -3 + -1x

Simplifying
0 = -3 + -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.