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

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

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

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

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

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

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

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

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

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

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

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

Solving
1 + 2lnx = lnx

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.
1 + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
1 + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1 + 1lnx = 0

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

Combine like terms: 1 + -1 = 0
0 + 1lnx = 0 + -1
1lnx = 0 + -1

Combine like terms: 0 + -1 = -1
1lnx = -1

Divide each side by '1nx'.
l = -1n-1x-1

Simplifying
l = -1n-1x-1