Question

Sabe-se que log 2 = 0,30103, Calcule:
log 25​

Answer 1

Olá Carlos!

Resposta:

$\boxed{\mathtt{1,39794}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\log 25 = \log 5^2} \\\\ \mathsf{\qquad \ \ = 2 \cdot \log 5} \\\\ \mathsf{\qquad \ \ = 2 \cdot \log \left ( \frac{10}{2} \right )} \\\\ \mathsf{\qquad \ \ = 2 \cdot \left ( \log 10 - \log 2 \right )} \\\\ \mathsf{\qquad \ \ = 2 \cdot \left ( 1 - 0,30103 \right )} \\\\ \mathsf{\qquad \ \ = 2 \cdot 0,69897} \\\\ \mathsf{\qquad \ \ = \boxed{\boxed{\mathsf{1,39794}}}}}$

Obs.:

$\\ \displaystyle \bullet \qquad \mathtt{\log_a b^c = c \cdot \log_a b} \\\\ \bullet \qquad \mathtt{\log_{10} 10 = \log_{10} 10^1 = 1 \cdot \log_{10} 10 = 1 \cdot 1 = 1}$