Given that a and B are positive real numbers, compare the size of (a) ^ a (b) ^ B with (AB) ^ (a + B / 2) Is there anything more understandable than the "quotient comparison method" that can be found now

Given that a and B are positive real numbers, compare the size of (a) ^ a (b) ^ B with (AB) ^ (a + B / 2) Is there anything more understandable than the "quotient comparison method" that can be found now

The logarithm method may be simpler. Compare the size of (a) ^ a (b) ^ B and (AB) ^ (a + B / 2), and convert it into the size of LG (a ^ a × B ^ b) and LG (AB) ^ (A / 2 + B / 2). LG (a ^ a × B ^ b) = alga + blgblg (AB) ^ (A / 2 + B / 2) = (a + b) / 2 LGA + (a + b) / 2 lgblg (a ^ a × B ^ b) - LG (AB) ^ (a / 2 + B / 2)