Question

se log2 x-co log4 x+log16 x=7 o valor de x é
a)4
b)16
c)8
d)32

Answer 1

$Ola'~~ \\ \\ Se: ~log_2x-colog_4x+log_{16}x=7 \\ \\ \underline{soluc\~ao~} \\ \\ log_2x-log_4 \frac{1}{x}+log_{16}x=7 \\ \\ log_2x+log_4x+log_{16}x=7 \\ \\ log_2x+ \frac{log_2x}{log_24}+ \frac{log_2x}{log_216}=7 \\ \\ log_2x+ \frac{log_2x}{2}+ \frac{log_2x}{4}=7 ~~--\ \textgreater \ M.M.C=4 \\ \\ \frac{4log_2x+2log_2x+log_2x}{4}=7 \\ \\ 7log_2x=7.(4) \\ \\ log_2x=4 \\ \\ \boxed{\boxed{x=16}} ~~---\ \textgreater \ alternativa~\textcircled{b}$

$\mathbb{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx} \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$