Question

A partir das propriedades, calcule o valor dos seguintes logaritmos: (dado log 2=0,3; log 3=0,48 e log 5=0,7)

A) log15 =

B) log360 =​

Answer 1

• A partir das propriedades dos logs, temos que:

a) 1,18

b) 2,56

Para resolver sua questão, devemos aplicar as seguintes propriedades:

$\large\displaystyle\begin{aligned} \log_a (b\cdot c) = \log _a b + \log_a c\end{aligned}$

$\large\displaystyle\begin{aligned} \log_a (b^c) = c\cdot \log _a b \end{aligned}$

Dado que ( log 2=0,3; log 3=0,48 e log 5=0,7 ). Logo:

$\large\displaystyle\begin{aligned} \log(15) = \log (3\cdot 5 )\end{aligned}$

$\large\displaystyle\begin{aligned} \log(15) = \log (3) + \log (5)\end{aligned}$

$\large\displaystyle\begin{aligned} \log(15) = 0,48 + 0,70\end{aligned}$

$\large\displaystyle\text{ \begin{aligned}\therefore \boxed{\boxed{\green{ \log(15) = 1,18}}}\end{aligned} }$

• Fazendo a mesma coisa com o log de 360.

$\large\displaystyle\begin{aligned} \log(360) = \log (2^3\cdot 3^2 \cdot 5 )\end{aligned}$

$\large\displaystyle\begin{aligned} \log(360) = \log (2^3) + \log (3^2) + \log(5 )\end{aligned}$

$\large\displaystyle\begin{aligned} \log(360) = 3\cdot \log (2) + 2\cdot \log (3) + \log(5 )\end{aligned}$

$\large\displaystyle\begin{aligned} \log(360) = 3\cdot ( 0,3)+ 2\cdot (0,48) + (0,70)\end{aligned}$

$\large\displaystyle\begin{aligned} \log(360) = (0,9)+ (0,96) + (0,70)\end{aligned}$

$\large\displaystyle\begin{aligned} \log(360) = (1,86) + (0,70)\end{aligned}$

$\large\displaystyle\text{ \begin{aligned} \therefore \boxed{\boxed{\green{\log(360) = 2,56}}}\end{aligned} }$

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