Question

If $3=k.2^r$ and $15=k.4^r$, then the value of $r$ will be

• A. ${\log }_{2}5$
• B. $2$
• C. ${\log }_{2}10$
• D. $4$

Answer 1

Answer: (A)

${\log }_{2}5$

Given, $3=k{.2}^r$ and $15=k{.4}^r$

We have, $15=k{.4}^r$
$\Rightarrow 3\times 5=k{.4}^r$
$\Rightarrow k{.2}^r\times 5=k{.4}^r$ .....$(\because 3=k{.2}^r)$
$\Rightarrow 2^r.5=2^{2r}$
$\Rightarrow 2^r=5$
$\Rightarrow r={\log }_{2}5$