Question

determine o valor dos logaritmos:

a) log (base 1/2) 7√16 = y


b) log (base 9) 3√10= y


c)log (base 4) √2 = y
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Answer 1

Resposta:

Explicação passo-a-passo:

a) log₁/₂ 7√16 = y

log₁/₂ 7.4 = y

log 7.4/log 1/2 = y

(log 7 + log 4)/log 2⁻¹ = y

y = (log 7 + log 2²)/log 2⁻¹

y = (log 7 + 2log 2)/(-log 2)

y = - (log 7 + 2log 2)/log 2

y = - (0,845 + 2.0,3)/0,3

y = - (1,445/0,3)

y = - 4,82.

b) log₉ 3√10 = y

log 3√10/log 9 =

(log 3 + log √10)/log 3² = y

(log 3 + (1/2)log 10)/2log 3 = y

y = (log 3 + 1/2)/2log 3

y = (0,477 + 1/2)/2(0,477)

y = 0,977/0,954

y = 1,024.

c)log₄ √2 = y

4^y = √2

2^2y = 2¹/²

2y = 1/2

y = 1/4.