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Show that the function f(x)=a^x ,\ 0<a<1...

Show that the function `f(x)=a^x ,\ 0

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Given,`f(x)=a^x` and `0 < a < 1`
is decreasing in R
Taking log both sides
`log f(x)=xloga`
`(f′(x))/(a^x)​=loga`
`f′(x)=a^x loga[a^x>0x∈R]`
`f(x)<0,x∈R`
⇒f(x) is decresing function [loga<0] because 0
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