Question

Considerando log3= 0,477, log5 = 0,699 e log2 5= 2,322 calcule
a) log2 20
b) log2 25

Answer 1

Observe ....log₂ 5=log 5 /log 2 = 2,322  ==>2,322*log 2= log 5

a)

#### log[a]  b  =log b / log a   ..........[a]  é a base

log₂ 20 =log 20 /log 2 

#### log (a*b) = log a + log b

#### log a^b  =b * log a

 = (log 2² * 5)/log2

 = (2*log2+log 5)/log 2

#### log₂ 5=log 5 /log 2 = 2,322  ==>log 5 =2,322*log 2

### substitui log 5 por 2,322*log 2

 = (2*log 2+log 5)/log 2

 = (2*log 2+ 2,322*log 2)/log 2

#### dividi tudo por log 2

 = 2+2,322 =4,322

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b) log2 25 = log2 5²   =2* log2 5  = 2 * 2,322 =4,644