Question

Log31+(log100)0,001/(log2 1/64 xlog4√8)

Answer 1

(log3)1 + log100 * log0,001 / (log2)1/64 * (log4)√8

Fazendo o Log de cada um

(log3)1=a
3^a=1
3^a=3^0
a=0    , logo (log3)1=0

log100=2

log0,001=c
10^c= 0,001
10^c=10^-4
c=-4      , logo log0,001= -4

(log2)1/64=d
2^d=1/64
2^d=64^-1
2^d=2^-6
d=-6     , logo (log2)1/64= -6

(log4)√8=e
4^e=√8
2^2e=8^1/2
2^2e=2^3/2
2e=3/2
e=3/4    , logo (log4)√8= 3/4

SUBSTITUINDO OS VALORES

(log3)1 + log100 * log0,001              0 +2 *(-4)
-----------------------------------   →       -------------   ∴ →  -8/-18 → 8/18 ou 0,44...
    (log2)1/64 * (log4)√8                      -6 * (3/4)

Espero ter ajudado!