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Prove that the function f(x)=(log)a x i...

Prove that the function `f(x)=(log)_a x` is increasing on `(0,oo)` if `a >1` and decreasing on `(0,oo),` if `0ltalt1`

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SHP(1) f(x)=`log_a​` x
f(x)= `log_e a`/`log_e​ x`
​ diff wrt x
f ′ (x)= `1/(log_e​ (a))` × `1/x` ​
f ′ (x)= `1/(xlog(a))`
​if a>1
then
f ′ (x)>0 ...
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