SOLUTION: solve the following equation: logbase4(s^2-9)-logbase4(x+3)=3 logbase9 x + 3 logbase3 x =14 Thank you so much!!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve the following equation: logbase4(s^2-9)-logbase4(x+3)=3 logbase9 x + 3 logbase3 x =14 Thank you so much!!      Log On


   

Question 7040: solve the following equation:
logbase4(s^2-9)-logbase4(x+3)=3
logbase9 x + 3 logbase3 x =14
Thank you so much!!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
1. log%28x%5E2-9%29-log%28x%2B3%29=3 base4 is assumed.
log%28%28x%5E2-9%29%2F%28x%2B3%29%29+=+3
%28%28x%2B3%29%28x-3%29%2F%28x%2B3%29%29+=+4%5E3
%28%28x%2B3%29%28x-3%29%2F%28x%2B3%29%29+=+64
%28x-3%29+=+64
--> x=67

2. logbase9 x + 3 logbase3 x = 14. I will convert the base9 to base3 and then everything will be base3.

logx%2Flog9+%2B+3log%28x%29+=+14
logx%2F2+%2B+3log%28x%29+=+14
logx+%2B+6log%28x%29+=+28
logx+%2B+log%28x%5E6%29+=+28
log%28x%2Ax%5E6%29+=+28
log%28x%5E7%29+=+28
%28x%5E7%29+=+3%5E28
--> x+=+%283%5E28%29%5E%281%2F7%29
--> x+=+3%5E4
--> x = 81

jon.