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sqrt(7)^log5 - sqrt(5)^log7

 Jun 24, 2017
 #1
avatar+98130 
+1

 

There's nothing here to "solve".....just to evaluate..

 

√7^(log 5) - √5^(log 7)  =

 

[7^(1/2)]^(log 5)   - [ 5^(1/2)]^(log 7)=

 

[ 7] ^[ (1/2)log(5) ] - [5]^[ (1/2)log(7)]

 

[7] ^ [log √5]  -  [5]^[log √7 ]     note that we can write

 

[10^(log7)]^[log5]  - [10^(log 5)]^[log 7]

 

10 ^(log7 * log 5)  - 10^(log 5 * log 7)  =

 

10^(log5 * log 7) - 10^(log 5 * log7)  =

 

0

 

 

Then.....it  appears that we have the property that

 

a^(log b)  - b^(log a)   = 0

 

 

cool cool cool

 Jun 24, 2017

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