remember
[tex] log_{b}m^{n}=nlog_{b}m [/tex]
[tex] 1/4log_{5}81=log_{5}81^{1/4}=log_{5}3 [/tex]
[tex] 1/2log_{5}64=log_{5}64^{1/2}=log_{5}8 [/tex]
we now have
[tex] log_{5}n=log_{5}3+log_{5}8 [/tex]
remember
[tex] log_{b}m+log_{b}n= log_{b}(mn)[/tex] so
[tex] log_{5}3+log_{5}8= log_{5}(3*8)=log_{5}24[/tex]
[tex] log_{5}n=log_{5}24 [/tex]
therefor n=24
