Question

Considerando log 2 = A e log 7 = B, pode-se afirmar que log 3,92 vale:

a) 2b+3a-1
B)2b+3a-2
c) 3b+2a-2
d) 3b+2a-1
e) 2b+3a

Answer 1

Vamos começar reescrevendo o logaritmando para que, posteriormente, possamos determinar o valor do log com auxílio das propriedades de logaritmos.

$\log3,92~=~\log\,\left(\dfrac{392}{100}\right)\\\\\\\log3,92~=~\log\,\left(\dfrac{2\cdot2\cdot2\cdot7\cdot7}{10\cdot 10}\right)\\\\\\Aplicando~a~propriedade~do~logaritmo~do~quociente:\\\\\\\log3,92~=~\log\,(2\cdot2\cdot2\cdot7\cdot7)~-~\log\,(10\cdot 10)\\\\\\Aplicando~a~propriedade~do~logaritmo~do~produto:\\\\\\\log3,92~=~\left(\log2+\log2+\log2+\log7+\log7\right)-\left(\log10+\log10\right)\\\\\\Substituindo~o~valor~dos~logaritmos:$

$\log3,92~=~\left(a+a+a+b+b\right)-\left(1+1\right)\\\\\\\log3,92~=~\left(3a+2b\right)-\left(2\right)\\\\\\\boxed{\log3,92~=~2b+3a-2}~~ \Rightarrow~Letra~B\\\\\\\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$