I have been preparing for some time on this kind of Olympiad problems like the ones attached below. I am generally interested in equations, inequalities with logarithms, exponents, radicals etc. that use several concepts: strictly increasing/decreasing functions, injective functions, invertible functions, inequalities, convex or concave functions, Jensen's inequality etc. , but if possible without derivatives, limits because I don't master those yet. I thought I'd ask here because I'm sure there are many former Olympians or current Olympic students who are preparing for high school Olympiads and may have valid suggestions. It's mandatory that the problems have author's solutions or complete solutions, because I'm learning by myself.This are the type of problems that I am looking for :
