ln(2x-6)=ln(x-3)

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Solution for ln(2x-6)=ln(x-3) equation: 


Simplifying
ln(2x + -6) = ln(x + -3)

Reorder the terms:
ln(-6 + 2x) = ln(x + -3)
(-6 * ln + 2x * ln) = ln(x + -3)
(-6ln + 2lnx) = ln(x + -3)

Reorder the terms:
-6ln + 2lnx = ln(-3 + x)
-6ln + 2lnx = (-3 * ln + x * ln)
-6ln + 2lnx = (-3ln + lnx)

Solving
-6ln + 2lnx = -3ln + lnx

Solving for variable 'l'.

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

Add '3ln' to each side of the equation.
-6ln + 3ln + 2lnx = -3ln + 3ln + lnx

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

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

Add '-1lnx' to each side of the equation.
-3ln + 2lnx + -1lnx = lnx + -1lnx

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

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

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

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