What is #(sqrt7^((log_7)400))#?

1 Answer
George C.
Nov 28, 2015

#20#

Explanation:

If #a, b, c > 0# then #a^(bc) = (a^b)^c#

and #a^(log_a b) = b#

So:

#sqrt(7)^(log_7 400)#

#=(7^(1/2))^(log_7 400)#

#=7^(1/2 log_7 400)#

#=7^((log_7 400)*1/2)#

#=(7^(log_7 400))^(1/2)#

#=400^(1/2)#

#=sqrt(400)#

#=20#

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