A logarithmic equation
Algebra
Level
5
The sum of all (positive) solutions of the equation
\[\log_{16}x +\log _x 16=\log_{512} x + \log_x {512}\]
can be written as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers. What are the last three digits of \(a+b\)?
by
Calvin Lin