ln(9x-3)-ln(x-1)=0

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Solution for ln(9x-3)-ln(x-1)=0 equation: 


Simplifying
ln(9x + -3) + -1ln(x + -1) = 0

Reorder the terms:
ln(-3 + 9x) + -1ln(x + -1) = 0
(-3 * ln + 9x * ln) + -1ln(x + -1) = 0
(-3ln + 9lnx) + -1ln(x + -1) = 0

Reorder the terms:
-3ln + 9lnx + -1ln(-1 + x) = 0
-3ln + 9lnx + (-1 * -1ln + x * -1ln) = 0
-3ln + 9lnx + (1ln + -1lnx) = 0

Reorder the terms:
-3ln + 1ln + 9lnx + -1lnx = 0

Combine like terms: -3ln + 1ln = -2ln
-2ln + 9lnx + -1lnx = 0

Combine like terms: 9lnx + -1lnx = 8lnx
-2ln + 8lnx = 0

Solving
-2ln + 8lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-1 + 4x) = 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 '(-1 + 4x)' equal to zero and attempt to solve:

Simplifying
-1 + 4x = 0

Solving
-1 + 4x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x = 0 + 1
4x = 0 + 1

Combine like terms: 0 + 1 = 1
4x = 1

Add '-4x' to each side of the equation.
4x + -4x = 1 + -4x

Combine like terms: 4x + -4x = 0
0 = 1 + -4x

Simplifying
0 = 1 + -4x

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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