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

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


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

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

Remove parenthesis around (3x)
-1ln + lnx = ln * 3x

Reorder the terms for easier multiplication:
-1ln + lnx = 3ln * x

Multiply ln * x
-1ln + lnx = 3lnx

Solving
-1ln + lnx = 3lnx

Solving for variable 'l'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(1 + 2x) = 0

Ignore the factor -1.

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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

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

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

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

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

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

Simplifying
0 = -1 + -2x

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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