Question

1 - calcula el valor de los siguientes logaritmos, siendo que log2=0.3 y log3=0.47
a)log 6
b)log 24
c)log 32
d)log 72
e)log 2/81
f)log√108

Answer 1

Log2=0,3 y Log3=0,47

a) log6=log2x3
=log2 + log3
=0,3 + 0,47
= 0,77

b) log24=log2^3x3
=log2^3 + log3
=3log2 + log3
= 3(0,3) + 0,47
= 0,9 + 0,47
= 1,37

c) log32=log2^5
=5log2
=5(0,3)
=1,5

d) log72=log2^3x3^2
=log2^3 + log3^2
=3log2 + 2log3
=3(0,3) + 2(0,47)
=0,9 + 0,94
=1,84

e) log2/81 = log2 - log81
= log2 - log3^4
= 0,3 - 4(0,47)
= 0,3 - 1,88
= -1,58

f) log(108)^(1/2) = (1/2)log108
=(1/2)log2^2x3^3
=(1/2)[2log2 + 3log3]
=(1/2)[2(0,3) + 3(0,47)]
=(1/2)[0,6 + 1,41]
=(1/2)[2,01]
=1,005