Question

calcular el logaritmo de 64 en base 3^√2.(raíz cubica de 2)

Answer 1

$Log_ { \sqrt[3]{2} } 64= x \\ \\ ( \sqrt[3]{2})^x=64 \\ \\ ( \sqrt[3]{2})^x=2^6 \\ \\ 2^{ (\frac{1}{3})^x}=2^6 \\ \\ 2^{ (\frac{x}{3})}=2^6 \to \frac{x}{3}=6\to x=6*3\to \boxed{x=18} \\ \\ Entonces \\ \\ Log_ { \sqrt[3]{2} } 64= \boxed{18}$

Espero que te sirva, salu2!!!!