Here 27y = 9/3y, 81y^2 = 9, y^2=9/81 , y^2= 1/9, y= √1/9, y= 1/3 so here the value of y is 1/3

Introduction:

In this problem, we are given the equation 27y = 9/3y and we need to find the value of y. To solve this equation, we will apply certain mathematical operations to isolate the variable y.

Step 1: Simplify the equation:

To begin, we need to simplify the equation by getting rid of any fractions. In this case, we have the fraction 9/3y. We can simplify this fraction by dividing 9 by 3, which gives us 3. Therefore, the equation becomes 27y = 3y.

Step 2: Isolate the variable:

Next, we want to isolate the variable y on one side of the equation. To do this, we can subtract 3y from both sides of the equation. This yields:

27y - 3y = 3y - 3y

Simplifying the equation further, we get:

24y = 0

Step 3: Solve for y:

Now that we have isolated the variable y, we can solve for its value. In this case, since we have 24y = 0, we can divide both sides of the equation by 24. This gives us:

24y/24 = 0/24

Simplifying further, we obtain:

y = 0

Conclusion:

The value of y in the equation 27y = 9/3y is 0.