Question

resolva as expressão abaixo:

lo5+log3+2.log2-log6=

Answer 1

$log5+log3+2.log2-log6=\\ \\ log5+log3+log2^2-log6=\\ \\ log5+log3+log4-log6=\\ \\ log\frac{5*3*4}{6}=log10=1$

Answer 2

Quando temos log de mesma base, a soma vira multiplicação e a subtração vira divisão. Exemplo:

$log\ a+\ log\ b = log\ a*b\\\\ log\ a-log\ b=log\ \frac{a}{b}$

Voltando:

$log\ 5+log\ 3+2\ log\ 2-log\ 6\\\\ log\ 5+log\ 3+2\ log\ 2-(log3*2)\\\\ log\ 5+log\ 3+2\ log\ 2-log\ 3-log\ 2\\\\ log\ 5+log\ 2\\\\ log\ 5*2\\\\ log\ 10\\\\ \boxed{\boxed{1}}$