ln(x-5)=ln(4x-23)

Solution for ln(x-5)=ln(4x-23) equation:

Simplifying
ln(x + -5) = ln(4x + -23)

Reorder the terms:
ln(-5 + x) = ln(4x + -23)
(-5 * ln + x * ln) = ln(4x + -23)
(-5ln + lnx) = ln(4x + -23)

Reorder the terms:
-5ln + lnx = ln(-23 + 4x)
-5ln + lnx = (-23 * ln + 4x * ln)
-5ln + lnx = (-23ln + 4lnx)

Solving
-5ln + lnx = -23ln + 4lnx

Solving for variable 'l'.

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

Add '23ln' to each side of the equation.
-5ln + 23ln + lnx = -23ln + 23ln + 4lnx

Combine like terms: -5ln + 23ln = 18ln
18ln + lnx = -23ln + 23ln + 4lnx

Combine like terms: -23ln + 23ln = 0
18ln + lnx = 0 + 4lnx
18ln + lnx = 4lnx

Add '-4lnx' to each side of the equation.
18ln + lnx + -4lnx = 4lnx + -4lnx

Combine like terms: lnx + -4lnx = -3lnx
18ln + -3lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
18ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(6 + -1x) = 0

Ignore the factor 3.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Add 'x' to each side of the equation.
-1x + x = -6 + x

Combine like terms: -1x + x = 0
0 = -6 + x

Simplifying
0 = -6 + x

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.