+0  
 
0
236
1
avatar

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

Guest Jun 24, 2017
Sort: 

1+0 Answers

 #1
avatar+79894 
+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

CPhill  Jun 24, 2017

6 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details