SOLUTION: if log{a}((x^3)/(y{z}^16))=Alog{a}(x)+Blog{a}(y)+Clog{a^2} A=? B=? C=?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: if log{a}((x^3)/(y{z}^16))=Alog{a}(x)+Blog{a}(y)+Clog{a^2} A=? B=? C=?      Log On


   

Question 193720: if log{a}((x^3)/(y{z}^16))=Alog{a}(x)+Blog{a}(y)+Clog{a^2}
A=? B=? C=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given expression


... Expand the log using the identity log%28b%2C%28x%2Fy%29%29=log%28b%2C%28x%29%29-log%28b%2C%28y%29%29


... ... Expand the second log using the identity log%28b%2C%28x%2Ay%29%29=log%28b%2C%28x%29%29%2Blog%28b%2C%28y%29%29


... Distribute


... Pull down the exponents using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


So


So A=3, B=-1 and C=-16