SOLUTION: (log v3 81)*(log v81 3)=1 I have not idea if this one is true or false. Any ideas?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: (log v3 81)*(log v81 3)=1 I have not idea if this one is true or false. Any ideas?      Log On


   

Question 32906: (log v3 81)*(log v81 3)=1 I have not idea if this one is true or false. Any ideas?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= log(base sqrt3) 81
Then (sqrt3)^x=81
(sqrt3)^x=3^4= (sqrt3)^8
Therefore x=8
Let y=log(base sqrt81) 3
then (sqrt81)^y=3
9^y=3
Therefore y=1/2
Question now becomes; Does xy=1 ?
Since 8(1/2) is not 1 the answer is "FALSE".
Cheers,
Stan H.