How do you solve 4^(log_4 (100)) ??

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4^(log_4 (100))

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Answer 1 · 2017-12-13T07:17:15

$100 .$ $100.$

Recall the following Definition of $log$ $log$ function :

$a^{x} = y \Leftrightarrow x = {log}_{a} y .$ $a^x=y iff x=log_ay.$

Substituting $x$ $x$ in the L.H.S., we get,

$a^{{log}_{a} y} = y .$ $a^(log_ay)=y.$

With $a = 4, and y = 100,$ $a=4, and y=100,$

$4^{{log}_{4} 100} = 100 .$ $4^(log_4 100)=100.$