Simplify $2^(3+5log_2x)$ ?

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Answer 1 · 2018-02-08T14:51:39

$2^(3+5log_2x)=8x^5$

Let $a^(log_ax)=u$ . Then taking logarithm to the base $a$ on both sides we get

$log_ax xxlog_aa=log_au$

or $log_au=log_ax$ and therefore $u=x$ i.e.

$a^(log_ax)=x$

Using this in $2^(3+5log_2x)$

= $2^3xx2^(5log_2x)$

= $2^3xx(2^(log_2x))^5$ - as $a^(mn)=(a^m)^n$ or $(a^n)^m$

= $8x^5$

Simplify 2^(3+5log_2x)2^(3+5log_2x)?