Question

Dados log 2=0,3010 e log 3=0,4771, calcule:
a) log 243
b) log√3
c) log 108
d) log 18
e) log³√3
f) log 16
g) log√2

Answer 1

a) log 243 = log 3 ^5 = 5. log 3 = 5 . 0,4771 = 2,3855
b) = log √3 = log 3 ^1/2 = 1/2 . log 3 = 1/2 . 0,4771 = 0,2386
c) log 108 = log 2² . 3³ = 2.log2 + 3 log3 = 2. 0,3010 + 3. 0,4771 = 0,6020 + 1,4313 = 2,0333
d) log 18 = log. 2 . log 3² = log 2 + 2log 3 = 0,3010 + 2. 0,4771 = 0,3010 + 0,9542 = 1,2552
e) log ∛3  = log 3 ^1/3 = 1/3 . log 3 = 1/3 . 0,4771 = 0,4771 : 3 = 0,1590
f) log 16 = log 2² . log 2² = 2 log 2 + 2 log 2 = 2. 0,3010 + 2.0,3010 = 0,6020 + 0,6020 = 1,2040
g) log √2 = log 2 ^1/2 = 1/2 . log 2 = 1/2 . 0,3010 = 0,3010 : 2 =0,1505