Question

Dados log 2=a e log 5=b , determine a) Log 10 B) log 100 c) log √50 d) log 0,8

Answer 1

a-) log 10 = log 2.5 = log 2 + log 5 = a+b

b-) log 100 = log 10² = 2.log 10 = 2.log 2.5 = 2.log 2 + 2.log 5 = 2.a+2.b = 2.(a+b)

c-) $log(\sqrt{50}) = log(50^{\frac{1}{2}}) =\frac{1}{2}.log(50) =  \frac{1}{2}.log(2.5^2)= \frac{1}{2}.log(2)+\frac{1}{2}.log(5^2)=\frac{1}{2}.log(2)+\frac{1}{2}.(2).log(5)= \frac{1}{2}.log(2)+log(5) = \frac{1}{2}.a+b$

d-) $log(0,8) = log(\frac{8}{10}) = log(8)-log(10) = log(2^3)-log(2.5) = 3.log(2) - log(2)-log(5) = 2.log(2) - log(5) = 2a-b$