SOLUTION: 6=2logx+1/3logy solve for x

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Question 417039: 6=2logx+1/3logy
solve for x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
6+=+2log%28%28x%29%29+%2B+%281%2F3%29log%28%28y%29%29
Let's start by getting rid of the fraction. Multiplying both sides by 3 we get:
18+=+6log%28%28x%29%29+%2B+log%28%28y%29%29
Next we will subtract log(y):
18+-+log%28%28y%29%29+=+6log%28%28x%29%29
Now we'll divide both sides by 6:
%2818+-+log%28%28y%29%29%29%2F6+=+log%28%28x%29%29
which will simplify to:
3+-+%28log%28%28y%29%29%2F6%29+=+log%28%28x%29%29
And last, we will rewrite the equation in exponential form. In general log%28a%2C+%28p%29%29+=+q is equivalent to p+=+a%5Eq. Using this pattern on your equation we get:
10%5E%283+-+%28log%28%28y%29%29%2F6%29%29+=+x
(Sometimes expressions like the one above do not display well in your browser. If this is the case. then picture the left side as a 10 with an exponent of 3+-+%28log%28%28y%29%29%2F6%29