Lor
2023 AIME I
Problem 2
Positive real numbers 
and 
satisfy the equations![\[\sqrt{\log_b n} = \log_b \sqrt{n} \qquad \text{and} \qquad b \cdot \log_b n = \log_b (bn).\]](https://latex.artofproblemsolving.com/e/1/8/e188ed1d68418cfaed35d91cc7b0f333a84f6b1b.png)
The value of is 
where 
and 
are relatively prime positive integers. Find 
Solution
Lor
2023 AIME I
Problem 2
Positive real numbers and satisfy the equationsThe value of is where and are relatively prime positive integers. Find
Solution