Question

URGENTE PROVA SOCORRO

Answer 1

Propriedades usadas

$a\cdot\log_cb=\log_cb^a\\\\\log_{a^c}b=\dfrac{1}{c}\cdot\log_ab\\\\\dfrac{1}{\log_ba}=\log_ab\\\\\log_bb=1$

Solução:

$E=\dfrac{1}{\log_{101}2020^4}+\dfrac{1}{\log_52020^4}+\dfrac{2}{\log_22020^4}\\\\E=1\cdot\log_{2020^4}101+1\cdot\log_{2020^4}5+2\cdot\log_{2020^4}2\\\\E=\log_{2020^4}101+\log_{2020^4}5+\log_{2020^4}2^2\\\\E=\log_{2020^4}(101\cdot5\cdot2^2\\\\E=\log_{2020^4}2020\\\\E=\dfrac{1}{4}\cdot\log_{2020}2020\\\\\boxed{\boxed{E=\dfrac{1}{4}}}$