How do you simplify $9^{{log}_{9} x}$ $9^(log_9x)$ ?

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Answer 1 · 2016-08-22T22:09:25

$9^{{log}_{9} x} = x$ $9^(log_9 x)=x$

Let $9^{{log}_{9} x} = u$ $9^(log_9 x)=u$ , then as $a^{n} = b$ $a^n=b$ means ${log}_{a} b = n$ $log_a b=n$ , we have

${log}_{9} u = {log}_{9} x$ $log_9 u=log_9 x$ .

Hence $u = x$ $u=x$ and $9^{{log}_{9} x} = x$ $9^(log_9 x)=x$

How do you simplify 9^(log_9x)9log9x9^(log_9x)?