(x-3)=ln(7x-23)-ln(x+1)

Solution for (x-3)=ln(7x-23)-ln(x+1) equation:

Simplifying
(x + -3) = ln(7x + -23) + -1ln(x + 1)

Reorder the terms:
(-3 + x) = ln(7x + -23) + -1ln(x + 1)

Remove parenthesis around (-3 + x)
-3 + x = ln(7x + -23) + -1ln(x + 1)

Reorder the terms:
-3 + x = ln(-23 + 7x) + -1ln(x + 1)
-3 + x = (-23 * ln + 7x * ln) + -1ln(x + 1)
-3 + x = (-23ln + 7lnx) + -1ln(x + 1)

Reorder the terms:
-3 + x = -23ln + 7lnx + -1ln(1 + x)
-3 + x = -23ln + 7lnx + (1 * -1ln + x * -1ln)
-3 + x = -23ln + 7lnx + (-1ln + -1lnx)

Reorder the terms:
-3 + x = -23ln + -1ln + 7lnx + -1lnx

Combine like terms: -23ln + -1ln = -24ln
-3 + x = -24ln + 7lnx + -1lnx

Combine like terms: 7lnx + -1lnx = 6lnx
-3 + x = -24ln + 6lnx

Solving
-3 + x = -24ln + 6lnx

Solving for variable 'x'.

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

Add '-6lnx' to each side of the equation.
-3 + -6lnx + x = -24ln + 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-3 + -6lnx + x = -24ln + 0
-3 + -6lnx + x = -24ln

Add '3' to each side of the equation.
-3 + -6lnx + 3 + x = 3 + -24ln

Reorder the terms:
-3 + 3 + -6lnx + x = 3 + -24ln

Combine like terms: -3 + 3 = 0
0 + -6lnx + x = 3 + -24ln
-6lnx + x = 3 + -24ln

Reorder the terms:
-3 + 24ln + -6lnx + x = 3 + -24ln + -3 + 24ln

Reorder the terms:
-3 + 24ln + -6lnx + x = 3 + -3 + -24ln + 24ln

Combine like terms: 3 + -3 = 0
-3 + 24ln + -6lnx + x = 0 + -24ln + 24ln
-3 + 24ln + -6lnx + x = -24ln + 24ln

Combine like terms: -24ln + 24ln = 0
-3 + 24ln + -6lnx + x = 0

The solution to this equation could not be determined.