Question

Calcule o valor da base de cada logaritmo:
a) loga81=4
b) loga1024=20
c) loga125=3
d) loga256=8

Answer 1

Resposta:

$loga81=4\\\\\frac{\log _{10}\left(a\right)\cdot \:81}{81}=\frac{4}{81}\\\\\log _{10}\left(a\right)=\frac{4}{81}\\\\a=10^{\frac{4}{81}}\\\\\\\\loga1024=20\\\\\frac{\log _{10}\left(a\right)\cdot \:1024}{1024}=\frac{20}{1024}\\\\\log _{10}\left(a\right)=\frac{5}{256}\\\\a=10^{\frac{5}{256}}\\\\\\\\loga125=3\\\\\frac{\log _{10}\left(a\right)\cdot \:125}{125}=\frac{3}{125}\\\\\log _{10}\left(a\right)=\frac{3}{125}\\\\a=10^{\frac{3}{125}}\\\\\\\\loga256=8$

$\frac{\log _{10}\left(a\right)\cdot \:256}{256}=\frac{8}{256}\\\\\log _{10}\left(a\right)=\frac{1}{32}\\\\a=\sqrt[32]{10}$