Question

Determine o valor da expressão:

log raiz de 2 na base 16 + log de 8 na base 2

Answer 1

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}log_{16}\ \sqrt{2} + log_{2}\ 8 = \\\\log_{16}\ \sqrt{2} = x \\16^x = 2^{ \frac{1}{2} }\\2^{4x} = 2^{ \frac{1}{2} }\\4x = \frac{1}{2}\\8x=1\\x= \frac{1}{8}\\\\log_2\ 8=x\\2^x=8\\x=3\\\\ \boxed{\boxed{\frac{1}{8}+ 3 = \frac{1+24}{8} = \frac{25}{8} }}\end{array}\right$

Espero ter ajudado. :))