Prove that 1/(log_2(pi))+1/(log_(pi)(2))> 2 I have tried in many ways and i could not do it.

Cyrus Travis

Cyrus Travis

Answered question

2022-10-30

Prove that 1 log 2 π + 1 log π 2 > 2
I have tried in many ways and i could not do it.

Answer & Explanation

Davin Meyer

Davin Meyer

Beginner2022-10-31Added 13 answers

Remember that the sum of a positive number and its reciprocal is never less than 2. That is, a + 1 a 2. Equality happens when a = 1
In this case, notice that l o g π 2 and log 2 π are reciprocals of each other. Hence, the conclusion.
Rubi Garner

Rubi Garner

Beginner2022-11-01Added 4 answers

By the base change formula for logs,
log π 2 = 1 log 2 π .
Thus
1 log 2 π + 1 log π 2 = 1 log 2 π + log 2 π = ( 1 log 2 π log 2 π ) 2 + 2 > 2.

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