Q31 / 60 · KVPY 2011 (SA) · Mathematics

Below are four equations in $x$. Assume that $0 < \mathrm{r} < 4$. Which of the following has the largest solution for $x$ ?

  • A
    $5\left(1+\frac{\mathrm{r}}{\pi}\right)^{\mathrm{x}}=9$
  • Correct answer
    B
    $5\left(1+\frac{\mathrm{r}}{17}\right)^{\mathrm{x}}=9$
  • C
    $5(1+2 r)^{x}=9$
  • D
    $5\left(1+\frac{1}{\mathrm{r}}\right)^{\mathrm{x}}=9$

Solution

Given $0 < r < 4$ in the given options $(\text { Base })^{x}=\frac{9}{5}$ for largest value of $x$, base should be minimum. $\therefore$ in option $\mathrm{B}$ base $\left(1+\frac{\mathrm{r}}{17}\right)$ is minimum for $0 < \mathrm{r} < 4$.

Hence, the correct answer is option: 'B'.

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