Question

URGENTE!!! 

Sendo log 2 = x, calcular log50.

Algumas resoluções dizem que é 2-x, gostaria de saber como chegar ao resultado certo.

Answer 1

$\large\textsf{Principais propriedades dos logaritmos:}\\\\\\\mathsf{P1.~~\ell og_a(b\cdot c)=\ell og_a b+\ell og_a c}\\\\\\\mathsf{P2.~~\ell og_a(\dfrac{b}{c})=\ell og_ab-\ell og_ac}\\\\\\\mathsf{P3.~~\ell og_ab^{\alpha}=\alpha\cdot\ell og_ab}\\\\\\\textsf{Mudan\c{c}a~de~base:}~~\fbox{ \mathsf{\ell og_ab=\dfrac{\ell og_ca}{\ell og_cb}} }$

$\textsf{Com essas no\c{c}\~oes fica f\'acil resolver o exerc\'icio:}\\\\\\\mathsf{\ell og50~\Leftrightarrow~\ell og(\frac{100}{2})~\Leftrightarrow~\ell og100-\ell og2~\Leftrightarrow~\ell og100-x~\Leftrightarrow~\fbox{ 2-x }}\\\\\\\textsf{Lembrando que quando a base est\'a impl\'icita, consideramos como sendo}\\\textsf{decimal, logo:}\\\\\mathsf{~\ell og100~\Leftrightarrow~\ell og_{10}100~\Leftrightarrow~10^y=100~\Leftrightarrow~10^y=10^2~\Leftrightarrow~y=2}$