Since bases of logarithms are same, we can multiply (x +4) by (x +1); log (x +4)+ log (x +1) ⇒ log (x +4) (x +1) ⇒ log (x²+5 x +4)=1Now convert it to exponent formassume base is 10) x²+5 x +4=10^1 x²+5 x +4=10 x²+5 x — 6=0Now we can factor it; x²+5 x — 6=0 ⇒ (x +6) (x — 1)=0So answer so far is x=-6 or 1. Plug them into initial equation and progress; You will see that -6 isn't possibleSo we are left with x=1