SOLUTION: Can you help me write this problem as a single logarithm? 4log(base b)2-(1/3)log(base 9) b^15+1 So far I have compressed it into: log (base b) 16-log (base 9) b^5 +1 If you can

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can you help me write this problem as a single logarithm? 4log(base b)2-(1/3)log(base 9) b^15+1 So far I have compressed it into: log (base b) 16-log (base 9) b^5 +1 If you can      Log On


   

Question 752962: Can you help me write this problem as a single logarithm?
4log(base b)2-(1/3)log(base 9) b^15+1
So far I have compressed it into:
log (base b) 16-log (base 9) b^5 +1
If you can help me thank you so much!
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
logb16 - log9b5 + 1

logb16 - 5·log9b + 1

on the middle term we use log%28P%2C%28Q%29%29=1%2Flog%28Q%2C%28P%29%29

logb16 - 5%2Flog%28b%2C9%29 + 1

For the 1 on the right we use logbb = 1

logb16 - 5%2Flog%28b%2C9%29 + logbb

Swap the 2nd and 3rd terms:

logb16 + logbb - 5%2Flog%28b%2C9%29 

logb16b - 5%2Flog%28b%2C9%29

To keep it from getting too messy. let A = logb9

logb16b - 5%2FA

Get the LCD and combine terms:

%28A%2Alog%28b%2C16b%29+-+5%29%2FA

%28log%28b%2C%2816b%29%5EA%29+-+5%29%2FA

expr%281%2FA%29%28log%28b%2C%2816b%29%5EA%29+-+5%29

Write 5 as logbb5

expr%281%2FA%29%28log%28b%2C%2816b%29%5EA%29+-+log%28b%2Cb%5E5%29%29

expr%281%2FA%29log%28b%2C%2816b%29%5EA%2Fb%5E5%29

log%28b%2C%28%2816b%29%5EA%2Fb%5E5%29%5E%281%2FA%29%29

log%28b%2C%2816b%2Fb%5E%28%225%2FA%22%29%29%29

Finally replace A by logb9

log%28b%2C%2816b%2Fb%5E%28%225%2Flogb9%22%29%29%29

That's a mess because you had mixed bases 
in the beginning.

Edwin