Question

o valor de ㏒₄ ( 2 ÷ ㏒₁₆4)

Answer 1

$\log_{4} \left(2\div \log_{16} 4}\right)$

Observe que:
$\log_{16} 4 = \dfrac{1}{2}$

Pois,
$16^{x}=4\ \ \Rightarrow \left(4^{2}\right)^x=4\ \ \Rightarrow 4^{2x}=4\ \ \Rightarrow 2x=1 \ \ \Rightarrow x=\dfrac{1}{2}$


Assim reescrevendo o log, teremos:

$\log_{4} \left(2\div \log_{16} 4}\right)=\log_{4}\dfrac{2}{\frac{1}{2}}=\log_{4} 2\cdot 2=\log_{4} 4=1$