Which is bigger 5^(√3) and 4^(√5)? How do you know which one is bigger between $5^\sqrt{3}$ and $4^\sqrt{5}$?
For my method I used in $2^\sqrt{3}$ and $3^\sqrt{2}$ I put both numbers in the function $f(x)=x^\sqrt{3}$ so $f(2^\sqrt{3})$ become $2^3$ which is equal to 8 and $f(3^\sqrt{2})$ become $3^\sqrt{6}$ and $3^\sqrt{6}>3^\sqrt{2}$ which is equal to 9 and 9>8 so $3^\sqrt{2}>2^\sqrt{3}$
But for this problem I don't know what I should multiply or is there any method besides that? Please kindly help. Thank you

Take both to the power of $\sqrt{5}$
$\left(5^\sqrt{3}\right)^\sqrt{5}=5^{\sqrt{15}}<5^{\sqrt{16}}=5^4=625$
$\left(4^\sqrt{5}\right)^\sqrt{5}=4^5=1024$
so we have that $4^\sqrt{5}>5^\sqrt{3}$
