Prove that: `log_3log_2log_(sqrt(5))(625)=1`

Prove that log_3log_2log_(sqrt3) 81=1

Prove that log_2log_2log_(2) 16 =1

Prove that : (log_(2)10)(log_(2)80)-(log_(2)5)(log_(2)160)=4 .

Prove that: (log_a(log_ba))/(log_b(log_ab))=-log_ab

Prove that (log_(2)8)/(log_(3)9) =3/2

Prove that log(1+2+3)=log1+log2+log3

Prove that log_(7) log_(7)sqrt(7sqrt((7sqrt7))) = 1-3 log_(7) 2 .

Prove that: (log_9 11)/(log_5 3) = (log_3 11)/(log_sqrt(5) 3).

Which of the following when simplified reduces to unity? (log)_(3/2)(log)_4(log)_(sqrt(3))81 (log)_2 6+(log)_2sqrt(2/3) -1/6(log)_(sqrt(3/2))((64)/(27)) (d) (log)_(7/2)(1+2-3-:6)

Prove that: 2^((sqrt((log)_a4sqrt(a b)+(log)_b4sqrt(a b))-sqrt((log)_a4sqrt(b/a)+(log)_b4sqrt(a/b))))dotsqrt((log)_a b)={2ifbgeqa >1 and 2^(log_a(b) if 1