Question

Calcule os logaritmos usando a propriedade do produto.
a) Log 2 ( 32.8. 64)
b) Log 5 (5.625.125 )
c) Log 7 ( 7.343.49)
d) Log 25 ( 625. 15625 )
e) Log 3 ( 27.243 )


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Answer 1

Resposta:

Explicação passo-a-passo:

a) Log₂ ( 32.8. 64)  =

Log₂ 32 + Log₂ 8 + Log₂ 64 =

Log₂ 2⁵ + Log₂ 2³ + Log₂ 2⁶ =

5Log₂ 2 + 3Log₂ 2 + 6Log₂ 2 =

5.1 + 3.1 + 6.1 =

14.

b) Log₅ (5.625.125 )  =

Log₅ (5.625.125 )  =

Log₅ 5 + Log₅ 625 + Log₅ 125 =

Log₅ 5 + Log₅ 5⁴ + Log₅ 5³ =

Log₅ 5 + 4Log₅ 5 + 3Log₅ 5 =

1 + 4.1 + 3.1 =

8.

c) Log₇ ( 7.343.49)  =

Log₇ 7 + Log₇ 343⁴ + Log₇ 49 =

Log₇ 7 + Log₇ 7³ + Log₇ 7² =

Log₇ 7 + 3Log₇ 7 + 2Log₇ 7 =

1 + 3 + 2 =

6.

d) Log₂₅ ( 625. 15625 )  =

Log₂₅ 625 + Log₂₅ 15625 =

Log₂₅ 25² + Log₂₅ 25³ =

2Log₂₅ 25 + 3Log₂₅ 25 =

2 + 3 =

5.

e) Log₃ ( 27.243 ) =

Log₃ 27 + Log₃ 243 =

Log₃ 3³ + Log₃ 3⁵ =

3Log₃ 3 + 5Log₃ 3 =

3 + 5 =

8.