Find $y - x$ where $x$ is the largest integer with $2^{x}

Question

Find $y - x$ where $x$ is the largest integer with $2^{x} < 10^{6}$ and $y$ is the smallest integer with $10^{6} < 2^{y}$.

Aicharya · Accepted Answer

$2^{19} = 524{,}288 10^{6}$. So $x = 19$, $y = 20$, hence $y - x = 1$.

Find $y - x$ where $x$ is the largest integer with $2^{x} < 10^{6}$ and $y$ is the smallest integer with…