SOLUTION: determine the value of b, c and d if log3(root x^b y^c / w^d ) = 3/2log3(x) + log3(y) - 1/2 log3(w) then show that d=bc-5 pls help me with this problem asap the whole fraction

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: determine the value of b, c and d if log3(root x^b y^c / w^d ) = 3/2log3(x) + log3(y) - 1/2 log3(w) then show that d=bc-5 pls help me with this problem asap the whole fraction      Log On


   

Question 1173506: determine the value of b, c and d if log3(root x^b y^c / w^d ) = 3/2log3(x) + log3(y) - 1/2 log3(w) then show that d=bc-5
pls help me with this problem asap the whole fraction is in the square root for the first log
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


Lets work with the left hand side (LHS) first:



+log%283%2C+sqrt%28x%5Eb%2Ay%5Ec%2Fw%5Ed%29+%29+

= +log%283%2C+%28%28x%5Eb%2Ay%5Ec%2Fw%5Ed%29%5E%281%2F2%29+%29%29+



Use property +%28a%5Ek%29%5Eh+=+a%5E%28kh%29+



= 



Now apply +log%28%28x%5Ey%29%29+=+y%2Alog%28%28x%29%29+  and  +log%28%28xy%29%29+=+log%28%28x%29%29+%2B+log%28%28y%29%29+



= 





Now compare this LHS to what they gave you for the RHS and you should be able to use simple calculations to get b,c, and d.