If $y=2^{a x}$ and $\left(\frac{d y}{d x}\right)_{x=1}=\log 256$, then $a=$

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Aicharya · Accepted Answer

$y=2^{2 x} \Rightarrow \frac{d y}{d x}=2^{2 x}(\log 2)(a)$ $	herefore\left(\frac{d y}{d x}ight)_{x=1}=\left(2^{a}ight)(a)(\log 2)$ As per condition given $\left(2^{a}ight)(a)(\log 2)=\log 256=\log (2)^{8}=8 \log 2$ $	herefore\left(2^{a}ight)(a)=8 \Rightarrow a=2$

If $y=2^{a x}$ and $\left(\frac{d y}{d x}\right)_{x=1}=\log 256$, then $a=$

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