2ln(x-1)=ln(4x-7)

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Solution for 2ln(x-1)=ln(4x-7) equation: 


Simplifying
2ln(x + -1) = ln(4x + -7)

Reorder the terms:
2ln(-1 + x) = ln(4x + -7)
(-1 * 2ln + x * 2ln) = ln(4x + -7)
(-2ln + 2lnx) = ln(4x + -7)

Reorder the terms:
-2ln + 2lnx = ln(-7 + 4x)
-2ln + 2lnx = (-7 * ln + 4x * ln)
-2ln + 2lnx = (-7ln + 4lnx)

Solving
-2ln + 2lnx = -7ln + 4lnx

Solving for variable 'l'.

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

Add '7ln' to each side of the equation.
-2ln + 7ln + 2lnx = -7ln + 7ln + 4lnx

Combine like terms: -2ln + 7ln = 5ln
5ln + 2lnx = -7ln + 7ln + 4lnx

Combine like terms: -7ln + 7ln = 0
5ln + 2lnx = 0 + 4lnx
5ln + 2lnx = 4lnx

Add '-4lnx' to each side of the equation.
5ln + 2lnx + -4lnx = 4lnx + -4lnx

Combine like terms: 2lnx + -4lnx = -2lnx
5ln + -2lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
5ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

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

Combine like terms: -2x + 2x = 0
0 = -5 + 2x

Simplifying
0 = -5 + 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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