ln(3x-1)=ln(2)+ln(x-2)+(x+1)

Solution for ln(3x-1)=ln(2)+ln(x-2)+(x+1) equation:

Simplifying
ln(3x + -1) = ln(2) + ln(x + -2) + (x + 1)

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

Reorder the terms for easier multiplication:
-1ln + 3lnx = 2ln + ln(x + -2) + (x + 1)

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

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

Remove parenthesis around (1 + x)
-1ln + 3lnx = 2ln + -2ln + lnx + 1 + x

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

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

Solving
-1ln + 3lnx = 1 + lnx + x

Solving for variable 'l'.

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.