Question

Sabendo log 2 = x e log 3 = y calcular a) log 24 B) log 9 ✔️8

Answer 1

Temos o seguinte:

$log \ 2 = x \\ log \ 3 = y$

Logo:

$log \ 24 = log \ (2^3*3) = log \ 2^3 + log \ 3 = 3*log \ 2 + log \ 3 \\ \\ log \ 24 = 3x + y \\ ---------- \\ log \ 9 \sqrt{8} = log \ (9*8^{ \frac{1}{2} }) = log \ 3^2 + log \ (2^3)^{ \frac{1}{2} } = (2*log \ 3) + (\frac{3}{2} * log \ 2) \\ \\2*y + ( \frac{3}{2}*x ) = 2y + \frac{3x}{2} = \frac{4y + 3x}{2}$