Question

If $y=2^{ax}$ and $\frac{dy}{dx}=\log 256$ at $x=1$ , then a=?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

Given that,

$y=2^{ax}$ …… (1)

$\frac{dy}{dx}=\log 256$ …… (2)

Differentiating equation (1) with respect to $x$ and we get,

Then,

$\frac{dy}{dx}=a{.2}^{ax}.\log 2$ …… (3)

By equation (2) and (3) to

$\log 256=$$a{.2}^{ax}.\log 2$

$\log 2^8=a{.2}^{ax}.\log 2$

$8\log 2=a{.2}^{ax}.\log 2$

$8=a{.2}^{ax}$

$2^3=a{.2}^{ax}$

As given $x=1$,

$2^2.2=a{.2}^{a\times 1}$ …… (4)

By Inspection, we see that, $a=2$ satisfies the equation (4),

$L.H.S.=a{.2}^a=2\times 2^2=8$

$R.H.S.=8$

So, $2$ is the correct answer.