SOLUTION: reduce this to a single logarithm: log(x^5y^4)-2log(x(y^1/3))-5log(x/y) I did it but got it wrong on some online homework i got: log((y^9)/(x^2(y^2/3)))

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: reduce this to a single logarithm: log(x^5y^4)-2log(x(y^1/3))-5log(x/y) I did it but got it wrong on some online homework i got: log((y^9)/(x^2(y^2/3)))      Log On


   

Question 687650: reduce this to a single logarithm:
log(x^5y^4)-2log(x(y^1/3))-5log(x/y)
I did it but got it wrong on some online homework i got:
log((y^9)/(x^2(y^2/3)))
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28x%5E5y%5E4%29+-+2%2Alog%28x%2A%28y%5E1%2F3%29%29+-+5%2Alog%28x%2Fy%29++
I'll take each term one at a time
+log%28x%5E5y%5E4%29+
+log%28+x%5E5+%29+%2B+log%28+y%5E4+%29+
+5%2Alog%28+x+%29+%2B+4%2Alog%28+y+%29+
-------------------------
+2%2Alog%28x%2A%28y%5E1%2F3%29%29+
+2%2Alog%28+x+%29+%2B+2%2Alog%28+y%5E%281%2F3%29+%29+
+2%2Alog%28+x+%29+%2B+%282%2F3%29%2Alog%28+y+%29+
--------------------------
++5%2Alog%28x%2Fy%29+
+5%2Alog%28+x+%29+-+5%2Alog%28+y+%29+
-----------------------
Putting these together with the right signs:

Now put like terms together

+-+2%2Alog%28+x+%29+%2B+%28+27%2F3+%29%2Alog%28+y+%29+-+%282%2F3%29%2Alog%28+y+%29+
+%2825%2F3%29%2Alog%28+y+%29+-+2%2Alog%28+x+%29+ answer
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It's VERY easy to slip up- hope I got it