Question

Calcule o valor das expressões :
a) 2^1+log2 3
b)2^2+3 log2 5

Answer 1

Pra resolver essas questões a gente vai precisar de algumas propriedades dos logaritmos:

$\displaystyle \fbox{ 1^{\underline{a}} propriedade} \\\\ log_{ a}{\,a} = 1$

$\displaystyle \fbox{ 2^{\underline{a}} propriedade} \\\\ log_{ c}{\,(a \cdot b)} = log_{ c}{\,a} + log_{ c}{\,b}$

$\displaystyle \fbox{ 3^{\underline{a}} propriedade} \\\\ log_{ c}{\,a^b} = b \cdot log_{ c}{\,a}$

$\displaystyle \fbox{ 4^{\underline{a}} propriedade} \\\\ \not{a}^{log_{ \not{a}}{b}} = b$

Item a:

$\displaystyle 2^{1 + log_{ 2}{3}}$

$\displaystyle 2^{log_{ 2}{2} + log_{ 2}{3}}$

$\displaystyle 2^{log_{2}{6}}$

$\displaystyle \mathbf{6}$

Item b:

$\displaystyle 2^{2+3 log_{ 2}{5}}$

$\displaystyle 2^{2 \cdot log_{ 2}{2} + 3 log_{ 2}{5}}$

$\displaystyle 2^{log_{ 2}{4} + 3 log_{2}{5}}$

$\displaystyle 2^{log_{ 2}{4} + log_{2}{5^3}}$

$\displaystyle 2^{log_{ 2}{4} + log_{2}{125}}$

$\displaystyle 2^{log_{2 }{\, 500}}$

$\displaystyle \mathbf{500}$

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