Question

1) Calcule o valor dos seguintes logaritmos:

a) log 64 • (na base 16)
16

b) log √5 • (na base 625)
625

c) log (0,000064) • (na base 5)
5

d) log ³√7 • (na base 49)
49

e) log 128 • (na base ⁵√2)
⁵√2

f) log 3 √3 • (na base 9)
9

Answer 1

Vamos lá

1) Calcule o valor dos seguintes logaritmos:

a) log16(64) = log(64)/log(16) = log(2^6)/log(2^4) = 6/4 = 3/2

b) log625(√5) = log(5)/2log(625) = log(5)/2*log(5^4) = 1/8

c) log5(0.000064) = log5(5^-6) = -6

d) log49(³√7) = log(7)/3log(49) = log(7)/3log(7^2) = 1/6

e) log⁵√2(128) = log(2^7)/log(2)/5 = 35

f) log9(3√3) = log(3)/2log(3) + log(3)/4log(3) = 1/2 + 1/4 = 3/4