Question

If $y=2^{ax}$ and $\frac{dy}{dx}=\log 256$ at $x=1$ then the value of $a$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is D 3

Here, $y=2^{ax}$

$y^1=2^{ax}\ln \left(2\right)={\log }_{e}250$

$2^a\log \left(2\right)=\log 256$

$log(2{)}^a=\log 256$

$(2{)}^{2^a}=(2{)}^8$

$\Rightarrow 2^a=8;a=3$.