Question

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

Answer 1

Answer: 2.00

$\log y=ax\log 2$
$\frac{1}{y}\frac{dy}{dx}=a\log 2$
$\frac{dy}{dx}=2^{ax}\cdot a\log 2$
${\frac{dy}{dx})}_{x=1}=2^a\cdot a\log 2=8\log 2$
$=2^a\cdot a=8;a=2$