Question

considere 2= 0,3 ; 3= 0,48.

log 36 na base 8.

Answer 1

Explicação passo-a-passo:

Você quis dizer: considere log2=0,3 e log3=0,48

$log_{8}(36) \\ log_{ {2}^{3} }(4 \times 9) \\ log_{ {2}^{3} }(4) + log_{ {2}^{3} }(9) \\ \frac{1}{3} log_{ 2 }(4) + \frac{1}{3} log_{ 2 }(9) \\ \frac{1}{3} log_{ 2 }( {2}^{2} ) + \frac{1}{3} log_{ 2 }( {3}^{2} ) \\ \frac{2}{3} log_{ 2 }(2) + \frac{2}{3} log_{ 2 }(3) \\ \frac{2}{3} \times 1 + \frac{2}{3} \times \frac{ log(3) }{ log(2) } \\ \frac{2}{3}+ \frac{2}{3} \times \frac{ 0.48 }{ 0.3} \\ \frac{2}{3} + \frac{0.96}{0.9} \\ \frac{2}{3} + \frac{96}{90} \\ \frac{2}{3} + \frac{16}{15} \\ \frac{15 \times 2 + 3 \times 16}{45} \\ \frac{30 + 48}{45} \\ \frac{78}{45} \\ 1.73333$