Question

sendo log 2=0,3 log 3=0,4 e log 5=0,7 calcule : log 50 base 2

Answer 1

$log_{2}50 = \frac{log 50}{log 2} = \frac{log 5.10}{log 2}= \frac{log5+log10}{log 2} = \frac{0,7+1}{0,3} = \frac{1,7}{0,3} \\ \\ \frac{1,7}{0,3} = \frac{ \frac{17}{10} }{ \frac{3}{10} } = \frac{17}{10} . \frac{10}{3} = \frac{17}{3} =5,66$

Espero ter ajudado.

Answer 2

Log 50 base 2  

Log 50= 2^x 

Log 50 = xLog2

Log5².2=x Log2

2Log5.2=x Log2

2(log5)+Log2
__________  = x 
     Log 2

Substitui os valores dos logs 

X=2(0,7)+0,3/0,3
X=1,4+0,3
X=1,7/0,3
X=5,66...  ou   17/3