log5(x)-log5(x+4)=-1 (the 5s are in the base of the log)

Question

I need to find x

I know you can combine them into log5(x/x+4)= -1 but i don't know what to do from there

Answer 1

log5(x)-log5(x+4)=-1
log5[ x/(x+4) ] = -1
now use your definition of logs
x/(x+4) = 5^-1 = 1/5
5x = x+4
4x = 4
x = 1

check:
LS = log₅ (1) - log₅ (5)
= 0 - 1
= -1
= RS