SOLUTION: Given that Log (base 4) 3y – 2 log (base 4) x – 1 = 0, express y in terms of x. I hope you get the question right!

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Question 823929: Given that Log (base 4) 3y – 2 log (base 4) x – 1 = 0, express y in terms of x.
I hope you get the question right!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C+%283y%29%29+-+2log%284%2C+%28x%29%29+-+1+=+0
First we will combine the logs. To do so we need to use a property of logarithms, n%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5En%29%29, to "move" the 2 in front of the second log:
log%284%2C+%283y%29%29+-+log%284%2C+%28x%5E2%29%29+-+1+=+0
Now we can use another property of logs, log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29, to combine the logs:
log%284%2C+%28%283y%29%2Fx%5E2%29%29+-+1+=+0

Now that we are down to one log, we will isolate it. Adding 1 to each side:
log%284%2C+%28%283y%29%2Fx%5E2%29%29+=+1
Next we rewrite the equation in exponential form. In general log%28a%2C+%28p%29%29+=+n is equivalent to p+=+a%5En. Using this pattern on our equation we get:
%283y%29%2Fx%5E2+=+4%5E1
which simplifies to:
%283y%29%2Fx%5E2+=+4

Now that the logs are gone, we can solve for y. Multiplying both sides by x%5E2:
3y+=+4x%5E2
Dividing by 3:
y+=+%284x%5E2%29%2F3