Question

Sabendo que log 3 = 0,477, determine log √27000

Answer 1

Resposta: 2,2155

Explicação passo-a-passo:

Precisa aplicar algumas propriedades de log.

$log\sqrt{27000} = log27000^{\frac{1}{2}} = \frac{1}{2}log27000 =\frac{1}{2}log(3^3*10^3) = \frac{1}{2}[log(3^3) +log(10^3)] = \frac{1}{2}[3*log(3) +3*log(10)]=\frac{1}{2}[3*0,477 +3*1]=\frac{1}{2}[1,431 +3]=\frac{1}{2}[4,431]=2,2155$

Answer 2

Explicação passo-a-passo:

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Lembrando que:

$\boxed{\log_{a}(b.c)=\log_{a}b+\log_{a}c}$

$\boxed{\log_{a}b^{c}=c.\log_{a}b}$

Temos que :

$\log3=\text{0,477}$

Calculando $\log\sqrt{27000}$:

$\log\sqrt{27000}=\log(27000)^{\frac{1}{2} } \\\\\log\sqrt{27000}=\dfrac{1}{2}. \log27000\\\\\log\sqrt{27000}=\dfrac{1}{2}. \log(3^{3}.1000 )\\\\\log\sqrt{27000}=\dfrac{1}{2}. (\log3^{3} +\log1000)\\\\\log\sqrt{27000}=\dfrac{1}{2}. (3.\log3+3)\\\\\log\sqrt{27000}=\dfrac{1}{2}. (3\ .\ \text{0,477}+3)\\\\\log\sqrt{27000}=\dfrac{1}{2}. (\text{1,431}+3)\\\\\log\sqrt{27000}=\dfrac{1}{2}\ .\ \text{4,431}\\\\\boxed{\boxed{\log\sqrt{27000}= \text{2,2155}}}$