Question

If $p=\frac{s}{(1+k{)}^n}$, then the value of $n$ is equal to

• A. $\log \frac{s}{p(1+k)}$
• B. $\frac{\log \frac{s}{p}}{\log (1+k)}$
• C. $\frac{\log s}{\log p(1+k)}$
• D. $\frac{\log p(1+k)}{\log \frac{s}{p}}$

Answer 1

The correct option is B $\frac{\log \frac{s}{p}}{\log (1+k)}$

$p=\frac{s}{(1+k{)}^n}$
$\Rightarrow (1+k{)}^n=\frac{s}{p}$
$\Rightarrow n\log (1+k)=\log \left(\frac{s}{p}\right)$, taking log both sides and $\log a^m=m\log a$
$\Rightarrow n=\frac{\log \frac{s}{p}}{\log (1+k)}$
Ans: B