ln(x+1)+ln(x+2)=ln(x-1)+ln(x+7)

Solution for ln(x+1)+ln(x+2)=ln(x-1)+ln(x+7) equation:

Simplifying
ln(x + 1) + ln(x + 2) = ln(x + -1) + ln(x + 7)

Reorder the terms:
ln(1 + x) + ln(x + 2) = ln(x + -1) + ln(x + 7)
(1 * ln + x * ln) + ln(x + 2) = ln(x + -1) + ln(x + 7)
(1ln + lnx) + ln(x + 2) = ln(x + -1) + ln(x + 7)

Reorder the terms:
1ln + lnx + ln(2 + x) = ln(x + -1) + ln(x + 7)
1ln + lnx + (2 * ln + x * ln) = ln(x + -1) + ln(x + 7)
1ln + lnx + (2ln + lnx) = ln(x + -1) + ln(x + 7)

Reorder the terms:
1ln + 2ln + lnx + lnx = ln(x + -1) + ln(x + 7)

Combine like terms: 1ln + 2ln = 3ln
3ln + lnx + lnx = ln(x + -1) + ln(x + 7)

Combine like terms: lnx + lnx = 2lnx
3ln + 2lnx = ln(x + -1) + ln(x + 7)

Reorder the terms:
3ln + 2lnx = ln(-1 + x) + ln(x + 7)
3ln + 2lnx = (-1 * ln + x * ln) + ln(x + 7)
3ln + 2lnx = (-1ln + lnx) + ln(x + 7)

Reorder the terms:
3ln + 2lnx = -1ln + lnx + ln(7 + x)
3ln + 2lnx = -1ln + lnx + (7 * ln + x * ln)
3ln + 2lnx = -1ln + lnx + (7ln + lnx)

Reorder the terms:
3ln + 2lnx = -1ln + 7ln + lnx + lnx

Combine like terms: -1ln + 7ln = 6ln
3ln + 2lnx = 6ln + lnx + lnx

Combine like terms: lnx + lnx = 2lnx
3ln + 2lnx = 6ln + 2lnx

Add '-2lnx' to each side of the equation.
3ln + 2lnx + -2lnx = 6ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
3ln + 0 = 6ln + 2lnx + -2lnx
3ln = 6ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
3ln = 6ln + 0
3ln = 6ln

Solving
3ln = 6ln

Solving for variable 'l'.

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

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

Combine like terms: 3ln + -6ln = -3ln
-3ln = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-3ln = 0

Divide each side by '-3'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.