2ln(x-1)=ln(5x)

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Solution for 2ln(x-1)=ln(5x) equation: 


Simplifying
2ln(x + -1) = ln(5x)

Reorder the terms:
2ln(-1 + x) = ln(5x)
(-1 * 2ln + x * 2ln) = ln(5x)
(-2ln + 2lnx) = ln(5x)

Remove parenthesis around (5x)
-2ln + 2lnx = ln * 5x

Reorder the terms for easier multiplication:
-2ln + 2lnx = 5ln * x

Multiply ln * x
-2ln + 2lnx = 5lnx

Solving
-2ln + 2lnx = 5lnx

Solving for variable 'l'.

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

Add '-5lnx' to each side of the equation.
-2ln + 2lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 2lnx + -5lnx = -3lnx
-2ln + -3lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-2ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(2 + 3x) = 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

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

Combine like terms: 3x + -3x = 0
0 = -2 + -3x

Simplifying
0 = -2 + -3x

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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