Question

(UEL)O valor da expressão abaixo é igual a :
$\dfrac{ log_{3}(1) + log(0.01) }{ log_{2}( \frac{1}{64} ) \cdot log_{4}( \sqrt{8} ) }$
a)4/15
b)1/3
c)4/9
d)3/5
e)2/3​

Answer 1

log 3 (1)=0

log (0,01)= log (10^-2)=-2

log 2 (1/64)=log 2 (64^-1)=log 2 (2^-6)=-6

log 4 (√8)= log 2² (2^3/2)=3/4

log3(1) + log(0,01)/log2(1/64)×log4(√8)=

0-2/-6×3/4=

-2/-18/4=

-8/18=

8/18=

4/9 //.

_______

Answer 2

Explicação passo-a-passo:

Log 3 (1)=a

3^a=1

3^a=3^0

a=0

_____

log 10 (0,01)=b

10^b=10^-2

b=-2

_____

log 4 (√8)=c

(2)^2c=(2)^3/2

2c=3/2

c=3/4

____

log 2 (1/64)=d

2^d= (2)^-6

d=-6

____

log 3 (1) +log10 (0,01)

|______________________|

log 2(1/64).log 4 (√8)

= > 0 +(-2)/(-6).(3/4)

= -2/-18/4

= -2/1÷(-18/4)

=-2/1.(4/-18)

= (-2).(4)/-18

= -8/-18

= 4/9

alternativa C*

espero ter ajudado!

bom dia !