A.P , G.P

1) If a>1 , b>1 then show that the min value of log_b a + log _a b is 2.

2) Show that the least value of 2 log ₁₀₀ a - log_a 0.0001 for a >1 is 4.

3) If x,y,z are positive then show that the min value of
X ^{logy - logz}+ Y^{logz- logx}+Z ^logx-logy is 3.

1 Answers

1. =log _ab+ 1/log _ab
= x + 1/x form
â‰¥2 applying AM â‰¥ GM.

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