Question

1) Calcule o valor da expressão log10 1000 + log3 9 é igual a
a) 1
b) 3
c) 9
d) 10
e) 5

Answer 1

Oie, Tudo Bom?

■ Resposta: Opção E.

$= log_{10}(1000) + log_{3}(9)$

$= log_{10}(10 {}^{3} ) + log_{3}(3 {}^{2} )$

$= 3 log_{10}(10) + 2 log_{3}(3)$

$= 3 \: . \: 1 + 2 \: . \: 1$

$= 3 + 2$

$\boxed { = 5}$

Att. YNGBOYMMIV

Answer 2

$\sf \large{\sf \ell og _{10}(1000)+\ell og_{3}(9)}\\\\\\\\\large{\sf \ell og _{10}(1000)=3}\\\\\\\\\boxed{\sf Fatorar\:o\:n\acute{u}mero~1000=10^3}\\\\\\\\\large{\sf \ell og _{10}\left(10^3\right) }\\\\\\\\\boxed{\sf Aplicar\:as\:propriedades\:dos\:logaritmos\quad \ell og _a\left(a^x\right)=x}\\\\\\\\\sf =3\\\\\\\\\sf \large{\ell og _3\left(9\right)}\\\\\\\\\sf \large{\boxed{\sf Fatorar\:o\:n\acute{u}mero\:\:9=3^2}}\\\\\\\\\large{\sf \ell og _3\left(3^2\right)}$

$\sf \large{\boxed{\sf Aplicar\:as\:propriedades\:dos\:logaritmos\quad \ell og _a\left(a^x\right)=x}}\\\\\\\\=2\\\\\\\\\sf 3+2\\\\\\\\\boxed{\sf S_1=\{5\}}$