Question

considere log2 a e log3=b calcule:

a) log 32
b) log81/raiz de 3
c) log8 raiz de 27

Answer 1

a) log 32 = log 2^5 = 5log 2 = 5b

b) log 81/√3 = log 3^4/3 = 4log 3/3 = 4b/3

Answer 2

$Ola'! \\ \\log2=a \\ log3=b \\ \\ a) \\ log32=log 2^{5}=5log2=\boxed{5a} \\ \\ b) \\ log \frac{81}{ \sqrt{3} } =log (3^{4}. 3^{- \frac{1}{2} })=log 3^{ \frac{7}{2} } = \frac{7}{2}log3=\boxed{ \frac{7}{2}b} \\ \\ c) \\ log(8. \sqrt{27})= log8+log \sqrt{27}=log 2^{3}+log 3^{3/2}=3log2+ \frac{3}{2}log3 \\ \\ ~~~~~~~~~~~~~~~=\boxed{3a+ \frac{3}{2}b}$