Question

Sabendo que log 2 ≃ 0,3 e log 5 ≃ 0,7, determinar o valor aproximado de:
A) log⁡(5/2)
B) log⁡20
C) log⁡√5

Answer 1

Para este exercício, vamos utilizar as propriedades de logaritmo para reescreve-los em função do dados fornecidos no enunciado (log2 e log5).

a)

$\log\left(\dfrac{5}{2}\right)~=\\\\\\Aplicando~a~propriedade~do~\underline{logaritmo~do~quociente}:\\\\\\=~\log5~-~\log2\\\\\\\underline{Substituindo}~os~valores:\\\\\\=~0,7~-~0,3\\\\\\=~\boxed{~0,4~}$

b)

$\log20~=\\\\\\\underline{Fatorando}~o~logaritmando:\\\\\\=~\log\left(2\cdot 2\cdot 5\right)\\\\\\Aplicando~a~propriedade~do~\underline{logaritmo~do~produto}:\\\\\\=~\log2~+~\log2~+~\log5\\\\\\\underline{Substituindo}~os~valores:\\\\\\=~0,3~+~0,3~+~0,7\\\\\\=~\boxed{~1,3~}$

c)

$\log\sqrt{5}~=\\\\\\Reescrevendo~o~radical~como~uma~potencia~de~expoente~fracionario:\\\\\\=~\log5^{\frac{1}{2}}\\\\\\Aplicando~a~propriedade~do~\underline{logaritmo~da~potencia}:\\\\\\=~\dfrac{1}{2}\cdot \log5\\\\\\\underline{Substituindo}~os~valores:\\\\\\=~\dfrac{1}{2}\cdot 0,7\\\\\\=~\boxed{~0,35~}\\\\\\\\\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$