ln(x-5)-5=ln(x)

Solution for ln(x-5)-5=ln(x) equation:

Simplifying
ln(x + -5) + -5 = ln(x)

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

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

Multiply ln * x
-5 + -5ln + lnx = lnx

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

Combine like terms: lnx + -1lnx = 0
-5 + -5ln + 0 = lnx + -1lnx
-5 + -5ln = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-5 + -5ln = 0

Solving
-5 + -5ln = 0

Solving for variable 'l'.

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

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

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

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

Divide each side by '-5n'.
l = -1n-1

Simplifying
l = -1n-1