SOLUTION: Without a calculator, show that {{{ 1/ log( 2, pi ) }}} + {{{ 1/log( 5, pi ) }}} > 2.

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Question 626329: Without a calculator, show that +1%2F+log%28+2%2C+pi+%29+ + +1%2Flog%28+5%2C+pi+%29+ > 2.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Without a calculator, show that +1%2F+log%28+2%2C+pi+%29+ + +1%2Flog%28+5%2C+pi+%29+ > 2.
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+1%2F+log%28+2%2C+pi+%29+ + +1%2Flog%28+5%2C+pi+%29+
= +1%2F%28ln%28pi%29%2Fln%282%29%29 + 1%2F%28ln%28pi%29%2Fln%285%29%29
= ln%282%29%2Fln%28pi%29 + ln%285%29%2Fln%28pi%29
= ln%2810%29%2Fln%28pi%29
= log%2810%29%2Flog%28pi%29
= 1/log(pi)
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pi+%3C+sqrt%2810%29
--> 1/(<0.5)
--> > 2