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(9)
a > b > 1, lga > 0, lgb > 0
(lga + lgb)/2 > √(lga*lgb), Q > P
Q = lg√(ab) < lg[(a + b)/2] = R
R > Q > P
(10)
a - b = (3ln2 - 2ln3)/6 = (ln8 - ln9)/6 < 0, a < b
a - c = (5ln2 - 2ln5)/10 = (ln32 - ln25)/10 > 0, a > c
b > a > c
a > b > 1, lga > 0, lgb > 0
(lga + lgb)/2 > √(lga*lgb), Q > P
Q = lg√(ab) < lg[(a + b)/2] = R
R > Q > P
(10)
a - b = (3ln2 - 2ln3)/6 = (ln8 - ln9)/6 < 0, a < b
a - c = (5ln2 - 2ln5)/10 = (ln32 - ln25)/10 > 0, a > c
b > a > c
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