ln(x-1)=ln(5)+ln(x-2)

Solution for ln(x-1)=ln(5)+ln(x-2) equation:

Simplifying
ln(x + -1) = ln(5) + ln(x + -2)

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

Reorder the terms for easier multiplication:
-1ln + lnx = 5ln + ln(x + -2)

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

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

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

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

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

Solving
-1ln = 3ln

Solving for variable 'l'.

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

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

Combine like terms: -1ln + -3ln = -4ln
-4ln = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-4ln = 0

Divide each side by '-4'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.