SOLUTION: 2Log Y base 3 + 2Log X base 3= 4, find y in terms of x?

Question 611748: 2Log Y base 3 + 2Log X base 3= 4, find y in terms of x?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To solve for y, we need to "extract" it from the logarithm. For this, let's start by using properties of logs to combine the two logs. First the coefficients have to go. The easy way for this is to divide both sides of the equation by 2:

Next we can use a property of logs, , to combine the logs. (This property requires logs with coefficients of 1. This is why the 2's had to go earlier.)

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

which simplifies to:
9 = y*x

Now that the logs are gone, the equation is simple to solve for y. Divide both sides by 9:

And we're finished!
RELATED QUESTIONS
Find y in terms of x when 2log of y to base 3 - 4 = 3log of (x+2) to base... (answered by MathLover1)

Find y in terms of x when 2log of y to base 3 - 4 = 3log of (x+2) to base... (answered by ewatrrr)

If log of (y + 1) to base 2 = 2log of x + c to base 2 and y = 3 when x = 2, find y in... (answered by greenestamps)

Write 2log base 2 t + 4log base 2 r-2/3 as a single logarithm Write log base 5... (answered by stanbon)

if log (in base 2) x + 2 = 2log ( in base 2) y. elExpress x in terms of... (answered by Alan3354)

1. 1/2log (base a) ^x + 3 log (base a) ^y - 3 log (base a) ^... (answered by Alan3354)

2log[base 3](x+4)-log[base... (answered by ewatrrr,stanbon)

Given that 2log to the base y of x =3 find the relation involving x and... (answered by stanbon)

2log base 3 of y +1/3 log base 3 of x - (log base 3 of 5 + 2 log base 3 of 3)... (answered by jsmallt9)