Question

1) Sendo log a = 4 log b = -2 log c = 3 Calcule a) log (a.b.c) = b) log a² . b³ / c = c) log a³ . b / c4 = d) log a / b³ .c4 =

Answer 1

Fórmulas:
$log(a \times b ) = log(a) + log(b)$
$log(a \div b) = log(a) - log(b)$
$log( {a}^{x} ) = x \times log(a)$


a)
$log(a \times b \times c ) = \\ log(a) + log(b) + log(c) = \\ 4 + ( - 2) + 3 = 5$
b)
$log( {a }^{2} \times {b}^{3} \div c ) = \\ 2 \times log(a) + 3 log(b) - log(c) = \\ 2 \times 4 + 3 \times ( - 2) - 3 = - 1$
c)
$log( {a}^{3} \times b \div {c}^{4} ) = \\ 3 log(a) + log(b) - 4 log(c) = \\ 3 \times 4 + ( - 2) - 4 \times 3 = - 2$
d)

$log(a \div {b}^{3} \times {c}^{4} ) = \\ log(a) - 3log(b) + 4 log(c) = \\ 4 - 3( - 2) + 4 \times 3 = 10$