2ln(x-1)=ln(-2x+17)

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Solution for 2ln(x-1)=ln(-2x+17) equation: 


Simplifying
2ln(x + -1) = ln(-2x + 17)

Reorder the terms:
2ln(-1 + x) = ln(-2x + 17)
(-1 * 2ln + x * 2ln) = ln(-2x + 17)
(-2ln + 2lnx) = ln(-2x + 17)

Reorder the terms:
-2ln + 2lnx = ln(17 + -2x)
-2ln + 2lnx = (17 * ln + -2x * ln)
-2ln + 2lnx = (17ln + -2lnx)

Solving
-2ln + 2lnx = 17ln + -2lnx

Solving for variable 'l'.

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

Add '-17ln' to each side of the equation.
-2ln + -17ln + 2lnx = 17ln + -17ln + -2lnx

Combine like terms: -2ln + -17ln = -19ln
-19ln + 2lnx = 17ln + -17ln + -2lnx

Combine like terms: 17ln + -17ln = 0
-19ln + 2lnx = 0 + -2lnx
-19ln + 2lnx = -2lnx

Add '2lnx' to each side of the equation.
-19ln + 2lnx + 2lnx = -2lnx + 2lnx

Combine like terms: 2lnx + 2lnx = 4lnx
-19ln + 4lnx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
-19ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-19 + 4x) = 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 '(-19 + 4x)' equal to zero and attempt to solve:

Simplifying
-19 + 4x = 0

Solving
-19 + 4x = 0

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

Add '19' to each side of the equation.
-19 + 19 + 4x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 4x = 0 + 19
4x = 0 + 19

Combine like terms: 0 + 19 = 19
4x = 19

Add '-4x' to each side of the equation.
4x + -4x = 19 + -4x

Combine like terms: 4x + -4x = 0
0 = 19 + -4x

Simplifying
0 = 19 + -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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