Question

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

• A. ${\log }_{2}5$
• B. ${\log }_{5}5$
• C. ${\log }_{8}5$
• D. None of these

Answer 1

Answer: (A)

${\log }_{2}5$

$3=K-2^r$ and $15=k-4^r$

$\Rightarrow K=\frac{3}{2^r}=\frac{15}{4^r}\Rightarrow \frac{4^r}{2^r}=5$

$\Rightarrow 2^r=5$ (Take $\log$ base 2)

$\Rightarrow r={\log }_{2}5$