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

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

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

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

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

Reorder the terms for easier multiplication:
lnx = -5ln + lnx + 5ln

Reorder the terms:
lnx = -5ln + 5ln + lnx

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

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

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

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

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.