Question

If $y=2^{ax}$ and $\frac{dy}{dx}=log256$ at $x=1$, then the value of a is?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

$y=2^{ax}$

$\Rightarrow lo{g}_2^y=ax$

$logy=\left(log2\right)ax$

$\Rightarrow \frac{1}{y}\frac{dy}{dx}=alog2$

$\Rightarrow \frac{1}{2^a}\times lo{g}_{256}=alo{g}_2\Rightarrow \frac{1}{2^a}\times 8lo{g}_2=alo{g}_2$

$8=a\times 2^a$

$\therefore a=2$.