Question

Qual o valor de x na equação Log2 x + log4 x = 6 ?

Answer 1

$Ol\acute{a}~~\mathbb{NANDA} \\ \\ seja~a~equac\tilde{a}o: \\ \\ Log_2x+log_4x=6~~Por~~--\ \textgreater \ propiedade~[log_ba= \frac{log_za}{log_zb}] \\ \\ log_2x+ \frac{log_2x}{log_24} =6 \\ \\ log_2x+ \frac{log_2x}{\underbrace{log_22 ^{2}}_{2} }=6 \\ \\ log_2x+ \frac{log_2x}{2}=6 \\ \\ 2log_2x+log_2x=12$

$3log_2x=12 \\ \\ log_2x=4 ~~---\ \textgreater \ por~propiedade~[log_ab=n=\ \textgreater \ a^{n}=b~] \\ \\ 2^{4}=x \\ \\\boxed{ \boxed{x=16} }~---\ \textgreater \ resposta \\ \\ \mathbb{ttttttttttttttttttttttttttttttttttt} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero ~ter~ajudado!!$