If x = l o g 5 3 + l o g 7 5 + l o g 9 7 , then x ≥ Options: A . &nbsp32 B . &nbsp1213 C . &nbsp3213 D . &nbspNone

Answer: Option C : C Apply A . M . ≥ G . M . ∴ x ≥ 3. ( l o g 5 3. l o g 7 5. l o g 9 7 ) 1 3 = 3 ( l o g 9 3 ) 1 3 = 3 ( l o g 3 2 3 ) 1 3 = 3 ( 1 2 ) 1 3

If x=log53+log75+log97, then x ≥

Question

x = l o g_{5} 3 + l o g_{7} 5 + l o g_{9} 7

, then x

\geq

Options:

A . 32

B . 1213

C . 3213

D . None

Answer: Option C
:
C
Apply

A . M . \geq G . M .

∴ x \geq 3. (l o g_{5} 3. l o g_{7} 5. l o g_{9} 7)^{\frac{1}{3}}

= 3 (l o g_{9} 3)^{\frac{1}{3}} = 3 (l o g_{3^{2}} 3)^{\frac{1}{3}} = 3 {(\frac{1}{2})}^{\frac{1}{3}}

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