ln(x)+ln(x+5)=ln(x+1)+ln(x+3)

Solution for ln(x)+ln(x+5)=ln(x+1)+ln(x+3) equation:

Simplifying
ln(x) + ln(x + 5) = ln(x + 1) + ln(x + 3)

Multiply ln * x
lnx + ln(x + 5) = ln(x + 1) + ln(x + 3)

Reorder the terms:
lnx + ln(5 + x) = ln(x + 1) + ln(x + 3)
lnx + (5 * ln + x * ln) = ln(x + 1) + ln(x + 3)
lnx + (5ln + lnx) = ln(x + 1) + ln(x + 3)

Reorder the terms:
5ln + lnx + lnx = ln(x + 1) + ln(x + 3)

Combine like terms: lnx + lnx = 2lnx
5ln + 2lnx = ln(x + 1) + ln(x + 3)

Reorder the terms:
5ln + 2lnx = ln(1 + x) + ln(x + 3)
5ln + 2lnx = (1 * ln + x * ln) + ln(x + 3)
5ln + 2lnx = (1ln + lnx) + ln(x + 3)

Reorder the terms:
5ln + 2lnx = 1ln + lnx + ln(3 + x)
5ln + 2lnx = 1ln + lnx + (3 * ln + x * ln)
5ln + 2lnx = 1ln + lnx + (3ln + lnx)

Reorder the terms:
5ln + 2lnx = 1ln + 3ln + lnx + lnx

Combine like terms: 1ln + 3ln = 4ln
5ln + 2lnx = 4ln + lnx + lnx

Combine like terms: lnx + lnx = 2lnx
5ln + 2lnx = 4ln + 2lnx

Add '-2lnx' to each side of the equation.
5ln + 2lnx + -2lnx = 4ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
5ln + 0 = 4ln + 2lnx + -2lnx
5ln = 4ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
5ln = 4ln + 0
5ln = 4ln

Solving
5ln = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
5ln + -4ln = 4ln + -4ln

Combine like terms: 5ln + -4ln = 1ln
1ln = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
1ln = 0

Divide each side by '1'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.