Question

10. Se o log2 = a e log3=b, Coloque em função de a e b os seguintes logaritmos. a)log6 b)log4 c)log√2 d)log5

Answer 1

a) log6 = log2.3 = log2 + log3 = a + b

b) log4 = log2.2 = log2 + log2 = a + a = 2a

c) log(raiz de 2) = log2^1/2 (log de 2 elevado a 1/2) = 1/2.log2 = a/2

d) log5 = log10/2 = log10 - log2 = 1 - a

Answer 2

Se
log2=a

log3=b

a)
log6= log2 +log3
log6= a +b

b)
log4=log2 + log2
log4= a + a
log4=2a

c)

$\log \sqrt{2} =log2^{ \frac{1}{2} }= \frac{1}{2} log 2= \frac{1}{2} a= \frac{a}{2}$

d)
log5=log10 ÷log5=log10 - (log3 +log2)= 1-(a+b)=1-a-b

ou

$log5= \frac{log10}{log5} = \frac{1}{log2+log3} = \frac{1}{a+b}$