Question

Let $k$ be a rational number which is $50$ times its own logarithm to the base $10$, then the value of $\frac{k}{20}$ is

Answer 1

According to the question,
$k=50{\log }_{10}k$
$\Rightarrow {10}^k=k^{50}$
$\Rightarrow {10}^{2k}=k^{50\times 2}$
$\Rightarrow {100}^k=k^{100}$
$\Rightarrow k=100$
Ans: 5