How do you simplify $2^{{log}_{2} (12)}$ $2^(log_2(12))$ ?

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Answer 1 · 2016-03-17T18:07:18

$2^{{log}_{2} (12)} = 12$ $2^(log_2(12)) = 12$

By definition, the base- $a$ $a$ log of a number $x$ $x$ is the value $y$ $y$ such that $a^{y} = x$ $a^y=x$ . That is to say

${log}_{a} (x) = y \Leftrightarrow a^{y} = x$ $log_a(x) = y <=> a^y = x$

Then, applying the definition, for any $a$ $a$ , we have $a^{{log}_{a} (x)} = x$ $a^(log_a(x)) = x$

In this case, that gives us $2^{{log}_{2} (12)} = 12$ $2^(log_2(12)) = 12$

How do you simplify 2log2(12)2^(log_2(12)) ?