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

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

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

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

Remove parenthesis around (-3 + x)
-3 + x + ln(x + -2) = ln(x + -7)

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

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

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

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

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

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

Solving
-3 + -2ln + x = -7ln

Solving for variable 'l'.

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

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

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

Combine like terms: -7ln + 7ln = 0
-3 + 5ln + x = 0

Add '3' to each side of the equation.
-3 + 5ln + 3 + x = 0 + 3

Reorder the terms:
-3 + 3 + 5ln + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5ln + x = 0 + 3
5ln + x = 0 + 3

Combine like terms: 0 + 3 = 3
5ln + x = 3

Add '-1x' to each side of the equation.
5ln + x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
5ln + 0 = 3 + -1x
5ln = 3 + -1x

Divide each side by '5n'.
l = 0.6n-1 + -0.2n-1x

Simplifying
l = 0.6n-1 + -0.2n-1x