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

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

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

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

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

Reorder the terms for easier multiplication:
1ln + lnx + -2ln + lnx + -1 * 2ln = ln(2x + -1)

Multiply -1 * 2
1ln + lnx + -2ln + lnx + -2ln = ln(2x + -1)

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

Combine like terms: 1ln + -2ln = -1ln
-1ln + -2ln + lnx + lnx = ln(2x + -1)

Combine like terms: -1ln + -2ln = -3ln
-3ln + lnx + lnx = ln(2x + -1)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(2x + -1)

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

Add '-2lnx' to each side of the equation.
-3ln + 2lnx + -2lnx = -1ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-3ln + 0 = -1ln + 2lnx + -2lnx
-3ln = -1ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-3ln = -1ln + 0
-3ln = -1ln

Solving
-3ln = -1ln

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
-3ln + ln = -1ln + ln

Combine like terms: -3ln + ln = -2ln
-2ln = -1ln + ln

Combine like terms: -1ln + ln = 0
-2ln = 0

Divide each side by '-2'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.