Question

Sabendo que log 2= 0,301 calcule log 5√512

Answer 1

Podemos começar fatorando o 512,

512 I 2
256 I 2
128 I 2
  64 I 2
  32 I 2
  16 I 2
    8 I 2
    4 I 2
    2 I 2
    1

2⁹

Logo,

$log~5~.~512^{ \frac{1}{2} } \\ \\ \\ log~5~+~log~512^{ \frac{1}{2} } \\ \\ \\ log~ \frac{10}{2} + \frac{1}{2} ~.~(log~2^9) \\ \\ \\ log~10~-~log~2~+ \frac{1}{2} (9~.~log~2) \\ \\ \\ 1-0,301+ \frac{1}{2}~.~2,709 \\ \\ \\ \frac{2-0,602+2,709}{2} = \frac{2+2,107}{2} = \frac{4,107}{2} =2,0535$