a)
log_327^2=log_3(3^3)^2=log_33^6=6
log_{\frac{1}{2}}\frac{1}{32}=log_{\frac{1}{2}}(\frac{1}{2})^5=5
log_416^4=log_4(4^2)^4=log_44^8=8
log_5125^3=log_5(5^3)^3=log_55^9=9
b)
log_3\sqrt[4]{27}=log_3(3^3)^{\frac{1}{4}}=log_33^{\frac{3}{4}}=\frac{3}{4}
log\sqrt[3]{10000}=log_{10}(10^4)^{\frac{1}{3}}=log_{10}10^{\frac{4}{3}}=
\frac{4}{3}=1\frac{1}{3}
log_2\sqrt[7]8=log_2\sqrt[7]{2^3}=log_22^{\frac{3}{7}}=\frac{3}{7}
log_381^7=log_3(3^4)^7=log_33^{28}=28