ln(2x-7)=ln(3x-9)

Solution for ln(2x-7)=ln(3x-9) equation:

Simplifying
ln(2x + -7) = ln(3x + -9)

Reorder the terms:
ln(-7 + 2x) = ln(3x + -9)
(-7 * ln + 2x * ln) = ln(3x + -9)
(-7ln + 2lnx) = ln(3x + -9)

Reorder the terms:
-7ln + 2lnx = ln(-9 + 3x)
-7ln + 2lnx = (-9 * ln + 3x * ln)
-7ln + 2lnx = (-9ln + 3lnx)

Solving
-7ln + 2lnx = -9ln + 3lnx

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.
-7ln + 9ln + 2lnx = -9ln + 9ln + 3lnx

Combine like terms: -7ln + 9ln = 2ln
2ln + 2lnx = -9ln + 9ln + 3lnx

Combine like terms: -9ln + 9ln = 0
2ln + 2lnx = 0 + 3lnx
2ln + 2lnx = 3lnx

Add '-3lnx' to each side of the equation.
2ln + 2lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 2lnx + -3lnx = -1lnx
2ln + -1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
2ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Add 'x' to each side of the equation.
-1x + x = -2 + x

Combine like terms: -1x + x = 0
0 = -2 + x

Simplifying
0 = -2 + 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.