First, let's expand the logarithms.
[tex]log _{5} 4+log_{4}5 = \frac{log4}{log5}+\frac{log5}{log4} [/tex]
This because [tex]log_{y}x [/tex] is equivalent to [tex] \frac{logx}{logy} [/tex]
From there, you need to use a calculator to find the exact numerical value.
[tex] \frac{log4}{log5}+\frac{log5}{log4} = 2.02231716359[/tex]
