SOLUTION: if log base 10 y=0.7 + 2*log base 10 x , express y in terms of x

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: if log base 10 y=0.7 + 2*log base 10 x , express y in terms of x      Log On


   

Question 833497: if log base 10 y=0.7 + 2*log base 10 x , express y in terms of x
Answer by hovuquocan1997(83) About Me  (Show Source):
You can put this solution on YOUR website!
You have a property of log like this : if the base of two log are the same, you have log(x) - Log(y) = Log (x/y)
By the way if the base is 10, you don't need to write the base, it's a rule in Math :)
So your question is:
log(y) = 0.7 + 2log(x)
You have another property you need to use here, it says a%2Alog%28x%29+=+log%28x%5Ea%29
So your equation becomes
log%28y%29+=+0.7+%2B+log%28x%5E2%29
log%28y%29+-+log%28x%5E2%29+=+0.7
log%28y%2F%28x%5E2%29%29+=+0.7
The base is 10, so you have
y%2F%28x%5E2%29+=+10%5E%280.7%29
y+=+10%5E%280.7%29%2A%28x%5E2%29
TA-DAH
:D