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!

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) (Show Source): You can put this solution on YOUR website!

First we will combine the logs. To do so we need to use a property of logarithms, , to "move" the 2 in front of the second log:

Now we can use another property of logs, , to combine the logs:

Now that we are down to one log, we will isolate it. Adding 1 to each side:

Next we rewrite the equation in exponential form. In general is equivalent to . Using this pattern on our equation we get:

which simplifies to:

Now that the logs are gone, we can solve for y. Multiplying both sides by :

Dividing by 3:

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