ln(x-3)=ln(2x-9)

Solution for ln(x-3)=ln(2x-9) equation:

Simplifying
ln(x + -3) = ln(2x + -9)

Reorder the terms:
ln(-3 + x) = ln(2x + -9)
(-3 * ln + x * ln) = ln(2x + -9)
(-3ln + lnx) = ln(2x + -9)

Reorder the terms:
-3ln + lnx = ln(-9 + 2x)
-3ln + lnx = (-9 * ln + 2x * ln)
-3ln + lnx = (-9ln + 2lnx)

Solving
-3ln + lnx = -9ln + 2lnx

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.
-3ln + 9ln + lnx = -9ln + 9ln + 2lnx

Combine like terms: -3ln + 9ln = 6ln
6ln + lnx = -9ln + 9ln + 2lnx

Combine like terms: -9ln + 9ln = 0
6ln + lnx = 0 + 2lnx
6ln + lnx = 2lnx

Add '-2lnx' to each side of the equation.
6ln + lnx + -2lnx = 2lnx + -2lnx

Combine like terms: lnx + -2lnx = -1lnx
6ln + -1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
6ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Add 'x' to each side of the equation.
-1x + x = -6 + x

Combine like terms: -1x + x = 0
0 = -6 + x

Simplifying
0 = -6 + x

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.