Question

$Se~~m=\log_516~.~\log_45 \\ \\ Qual ~~o~~valor~~de~~m$

Answer 1

Veja que : 

$\boxed{log_a\ b\ .\ log_b\ c\ =\ log_a\ c}$


reescrevendo ... 


$m=log_5\ 16\ .\ log_4\ 5\\\\\\m=log_4\ 5\ .\ log_5\ 16$


Assim temos que : 

$log_4\ 5\ .\ log_5\ 16=\boxed{log_4\ 16}$


Resolvendo ... 

$log_4\ 16=m\\\\\\16=4^{m}\\\\\\4^{2}=4^{m}\\\\\\\boxed{\boxed{m=2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$

Answer 2

Resposta:

$m = \log_5(16) \times \log_4(5) \\ m = \log_5(4^2) \times \log_4(5) \\ m = 2\log_5(4) \times \log_4(5) \\ m = 2 \times 1 \\ m = 2$

Espero Ter Ajudado !!