Question

1. Calcule o valor numérico de:

a) log100 0,01

b) log8 1024


Me ajudem!!

4699fc183a94b2dafe3da3aedb71a86e.docx

Answer 1

$\boxed{\log{a^n}=n\log{a}}$

$\boxed{\log_b{a}=\dfrac{\log_k{a}}{\log_k{b}}=\dfrac{\ln{a}}{\ln{b}}}$

a)

$\log_{100}{0.01}=\log_{10^2}{10^{-2}}=\dfrac{\log{10^{-2}}}{\log{10^2}}=-\dfrac{2\log{10}}{2\log{10}}=\boxed{-1}$

b)

$\log_8{1024}=\log_{2^3}{2^{10}}=\dfrac{\log_2{2^{10}}}{\log_2{2^3}}=\dfrac{10\log_2{2}}{3\log_2{2}}=\boxed{\dfrac{10}{3}}$