Question

log base 2 of (x+5) + log base 2 of (x+4)= log base 2 of 2

Answer 1

since the base of log 2 is uniform
i just omit writing it
hence the question goes
log(x+5) +log(x+4)=log2
thus log(x+5)(x+4)=log2
taking antilog both sides wrt common base 2 as mentioned we have
(x+5)(x+4)=2
x^2+9x+20-2=0
x^2+9x+18=0
x^2+6x+3x+18=0
x(x+6)+3(x+6)=0
or (x+6)(x+3)=0
hence x=-3,-6
but putting x=-6 in the question we have log(x+5)=log(-1) (absurd)
hence x=-3

Answer 2

rem
log a+ log b=logab (provided base of log is uniform throughout)

Answer 3

but if you plug -6 and -3 back in you get log 2