Question

Sendo log 2=0,3 e log 3= 0,4, calcule Log √24 ?

Answer 1

$log (\sqrt{24})=log(24)^ \frac{1}{2} = \frac{log(24)}{2} =\frac{log(2*2*2*3)}{2}=$

$\frac{log(2)+log(2)+log(2)+log(3)}{2}$

$\frac{0,3+0,3+0,3+0,4}{2}$

$\frac{1,3}{2} =0,65$

Answer 2

√24=√8·3=√8·√3
Colocando sob a forma de expoente temos
(2³)^1/2 + 3^1/2
Passando o log
log [(2³)^1/2 + 3^1/2]
log (2³)^1/2 +  log 3^1/2
1/2·log 2³+1/2 log 3
1/2·3·log2 + 1/2·log3
1/2·3·0,3 + 1/2·0,4=0,65