Ln(x+7)+ln(x-3)=ln(x)+ln(2)

Solution for Ln(x+7)+ln(x-3)=ln(x)+ln(2) equation:

Simplifying
Ln(x + 7) + ln(x + -3) = ln(x) + ln(2)

Reorder the terms:
nL(7 + x) + ln(x + -3) = ln(x) + ln(2)
(7 * nL + x * nL) + ln(x + -3) = ln(x) + ln(2)
(7nL + nxL) + ln(x + -3) = ln(x) + ln(2)

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

Reorder the terms:
-3ln + lnx + 7nL + nxL = ln(x) + ln(2)

Multiply ln * x
-3ln + lnx + 7nL + nxL = lnx + ln(2)

Reorder the terms for easier multiplication:
-3ln + lnx + 7nL + nxL = lnx + 2ln

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

Add '-1lnx' to each side of the equation.
-3ln + lnx + 7nL + -1lnx + nxL = 2ln + lnx + -1lnx

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

Combine like terms: lnx + -1lnx = 0
-3ln + 0 + 7nL + nxL = 2ln + lnx + -1lnx
-3ln + 7nL + nxL = 2ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-3ln + 7nL + nxL = 2ln + 0
-3ln + 7nL + nxL = 2ln

Solving
-3ln + 7nL + nxL = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
-3ln + 7nL + -2ln + nxL = 2ln + -2ln

Reorder the terms:
-3ln + -2ln + 7nL + nxL = 2ln + -2ln

Combine like terms: -3ln + -2ln = -5ln
-5ln + 7nL + nxL = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-5ln + 7nL + nxL = 0

Add '-7nL' to each side of the equation.
-5ln + 7nL + -7nL + nxL = 0 + -7nL

Combine like terms: 7nL + -7nL = 0
-5ln + 0 + nxL = 0 + -7nL
-5ln + nxL = 0 + -7nL
Remove the zero:
-5ln + nxL = -7nL

Add '-1nxL' to each side of the equation.
-5ln + nxL + -1nxL = -7nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-5ln + 0 = -7nL + -1nxL
-5ln = -7nL + -1nxL

Divide each side by '-5n'.
l = 1.4L + 0.2xL

Simplifying
l = 1.4L + 0.2xL