b)
log_416\sqrt4=log_44^2*4^{\frac{1}{2}}=log_44^{2\frac{1}{2}}=2\frac{1}{2}
c)
log_5\frac{\sqrt[3]{5^8}}{5}=log_5\frac{5^{\frac{8}{3}}}{5^1}=log_55^{\frac{8}{3}-\frac{3}{3}}=log_55^{\frac{5}{3}}=\frac{5}{3}=1\frac{2}{3}
d)
log_42+log_48=log_4(2*8)=log_416=log_44^2=2
e)
log_236-2log_23=log_236-log_23^2=log_2(36:9)=log_24=log_22^2=2