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

Answer: (B)

1

$y=2^{ax}$

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

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

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

$\Rightarrow \frac{1}{2^a}\times log256=alog2\Rightarrow \frac{1}{2^a}\times 8log2=alog2$

$8=a\times 2^a$

$\therefore a=2$.