solve the following equation show all work log4(x-4)= -1.

Answer 1

by definition:

log₄ (x-4) = -1
is equivalent to
x-4 = 4^-1
x-4 = 1/4
x = 1/4 - 4
= -15/4

so we would have log (-3/4-4)
but we cannot take the log of a negative, so ....
no solution.

Answer 2

log takes on all real values for its range. So, something's wrong here.

x - 4 = 1/4
x = 1/4 + 4
x = 17/4

log₄(17/4 - 4) = log₄(1/4) = -1