SOLUTION: find the value of a - b 5log x+ 1/3log y - 1/2log x - 5/6 log y= log(x^a y^b)

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Question 886329: find the value of a - b
5log x+ 1/3log y - 1/2log x - 5/6 log y= log(x^a y^b)
Found 3 solutions by lwsshak3, MathTherapy, greenestamps:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of a - b
5log x+ 1/3log y - 1/2log x - 5/6 log y- log(x^a y^b)=0
log%28%28x%5E5y%5E%281%2F3%29%2Fx%5E%281%2F2%29y%5E%285%2F6%29x%5E%28a%29y%5E%28b%29%29%29=0
log%28%28x%5E5%2Fx%5E%281%2F2%29y%5E%281%2F2%29x%5E%28a%29y%5E%28b%29%29%29=0
log%28%28x%5E5%2Fx%5E%28a%2B1%2F2%29y%5E%28b%2B1%2F2%29%29%29=0
%28x%5E5%2Fx%5E%28a%2B1%2F2%29y%5E%28b%2B1%2F2%29%29=1
x%5E5=x%5E%28a%2B1%2F2%29y%5E%28b%2B1%2F2%29
sorry, this is as far I can go
can't figure the value of a-b

Answer by MathTherapy(10862) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of  a - b
5log x+ 1/3log y - 1/2log x - 5/6 log y= log(x^a y^b)
*****************************************************


                             
                               
                                    
                                    
                                      
                                         ------ Applying log+%28b%2C+%28c%29%29+%2B+log+%28b%2C+%28d%29%29 = log+%28b%2C+%28cd%29%29
                                                     ---- EQUATING LOG-ARGUMENTS 
                                                                  

The other person who responded: lwsshak3(11628), is LOST. This author can't understand why he/she couldn't figure this out, 
leading to him/her stating: "sorry, this is as far I can go
                                                 can't figure the value of a-b"

Answer by greenestamps(13374) About Me  (Show Source):
You can put this solution on YOUR website!




Combine like terms on the left...

%289%2F2%29log%28x%29-%281%2F2%29log%28y%29=log%28%28%28x%5Ea%29%28y%5Eb%29%29%29

... and rewrite the expression on the right using laws of logarithms

%289%2F2%29log%28x%29-%281%2F2%29log%28y%29=%28a%29log%28x%29%2B%28b%29log%28y%29

Equate coefficients of log(x) and log(y) on the two sides

a=9%2F2; b=-1%2F2

Evaluate the expression you are asked to evaluate

a-b=%289%2F2%29-%28-1%2F2%29=10%2F2=5

ANSWER: 5