Question

URGENTE

Assumindo que log2=0,3 e log3=0,48.Calcule: log de 3 na base 2. *

2 pontos

1,5?

1,6?

Assumindo que log2=0,3 e log3=0,48.Calcule: log de 10 na base 3. *

2 pontos

2,08333...?

2,0?

Assumindo que log2=0,3 e log3=0,48.Calcule: log de 9 na base 8. *

2 pontos

1,06555...?

1,0666...?

Sabendo que log 2 = 0,301 , log 3 = 0,477 e log 7 = 0,845. Qual o valor de log de 7 na base 3? *

2 pontos

2,771?

1,771?

Sabendo que log 2 = 0,301 , log 3 = 0,477 e log 7 = 0,845. Qual o valor de log de 21 na base 7? *

2 pontos

1,262?

2,343?

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Answer 1

Mudança de base

$\huge \boxed{\boxed{\boxed{\mathsf{log_{b}a=\dfrac{log_{m}a}{log_{m}b}}}}}$

1)

$\mathsf{log_{2}3=\dfrac{log3}{log2}=\dfrac{0,48}{0,3}}\\\boxed{\boxed{\boxed{\mathsf{log_{2}3=1,6}}}}$

2)

$\mathsf{log_{3}10=\dfrac{log10}{log3}=\dfrac{1}{0,48}}\\\boxed{\boxed{\boxed{\mathsf{log_{3}10=2,08}}}}$

3)

$\mathsf{log_{8}9=\dfrac{log9}{log8}=\dfrac{2log3}{3log2}}\\\mathsf{log_{8}9=\dfrac{2.0,48}{3.0,3}}\\\boxed{\boxed{\boxed{\mathsf{log_{8}9=1,0666... }}}}$

4)

$\mathsf{log_{3}7=\dfrac{log7}{log3}=\dfrac{0,845}{0,477}}\\\boxed{\boxed{\boxed{\mathsf{log_{3}7=1,771}}}}$

5)

$\mathsf{log_{7}21=\dfrac{log21}{log7}=\dfrac{log(3.7)}{log7}}\\\mathsf{log_{7}21=\dfrac{log3+log7}{log7}} \\ \mathsf{=\dfrac{0,477+0,845}{0,845}}$

$\mathsf{log_{7}21=\dfrac{1,322}{0,845}} \\\boxed{\boxed{\boxed{\mathsf{log_{7}21=1,564}}}}$