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If $y=2^{a x}$ and $\left(\frac{d y}{d x}\right)_{x=1}=\log 256$, then $a=$
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The correct answer is:
2
$y=2^{2 x} \Rightarrow \frac{d y}{d x}=2^{2 x}(\log 2)(a)$
$\therefore\left(\frac{d y}{d x}\right)_{x=1}=\left(2^{a}\right)(a)(\log 2)$
As per condition given
$\left(2^{a}\right)(a)(\log 2)=\log 256=\log (2)^{8}=8 \log 2$
$\therefore\left(2^{a}\right)(a)=8 \Rightarrow a=2$
$\therefore\left(\frac{d y}{d x}\right)_{x=1}=\left(2^{a}\right)(a)(\log 2)$
As per condition given
$\left(2^{a}\right)(a)(\log 2)=\log 256=\log (2)^{8}=8 \log 2$
$\therefore\left(2^{a}\right)(a)=8 \Rightarrow a=2$
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