Filipjack 05.04.2024 01:28 Solve over the real numbers the equation $$3^{\log_5(5x-10)}-2=5^{-1+\log_3x}.$$
Maheshwarananda 05.04.2024 12:51 The LHS it is concave function, the RHS it is convex function, so we have maximum 2 solutions, and $x=3, x=27$ there are solutions! See for example https://www.wolframalpha.com/input?i=3%5Elog_5%285x-10%29%7D-2%3D5%5E%28-1%2Blog_3x%29