2ln(x-1)=ln(-3x+21)

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Solution for 2ln(x-1)=ln(-3x+21) equation: 


Simplifying
2ln(x + -1) = ln(-3x + 21)

Reorder the terms:
2ln(-1 + x) = ln(-3x + 21)
(-1 * 2ln + x * 2ln) = ln(-3x + 21)
(-2ln + 2lnx) = ln(-3x + 21)

Reorder the terms:
-2ln + 2lnx = ln(21 + -3x)
-2ln + 2lnx = (21 * ln + -3x * ln)
-2ln + 2lnx = (21ln + -3lnx)

Solving
-2ln + 2lnx = 21ln + -3lnx

Solving for variable 'l'.

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

Add '-21ln' to each side of the equation.
-2ln + -21ln + 2lnx = 21ln + -21ln + -3lnx

Combine like terms: -2ln + -21ln = -23ln
-23ln + 2lnx = 21ln + -21ln + -3lnx

Combine like terms: 21ln + -21ln = 0
-23ln + 2lnx = 0 + -3lnx
-23ln + 2lnx = -3lnx

Add '3lnx' to each side of the equation.
-23ln + 2lnx + 3lnx = -3lnx + 3lnx

Combine like terms: 2lnx + 3lnx = 5lnx
-23ln + 5lnx = -3lnx + 3lnx

Combine like terms: -3lnx + 3lnx = 0
-23ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-23 + 5x) = 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 '(-23 + 5x)' equal to zero and attempt to solve:

Simplifying
-23 + 5x = 0

Solving
-23 + 5x = 0

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

Add '23' to each side of the equation.
-23 + 23 + 5x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 5x = 0 + 23
5x = 0 + 23

Combine like terms: 0 + 23 = 23
5x = 23

Add '-5x' to each side of the equation.
5x + -5x = 23 + -5x

Combine like terms: 5x + -5x = 0
0 = 23 + -5x

Simplifying
0 = 23 + -5x

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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