9^2y * 2^x = 72
Value of x and y
9^2y * 2^2 = 3^2 * 2^3
9^2y * 2^2 = 9^1 *2^3
y = 1/2
x = 3
9^2(1/2) * 2^3 = 72
9* 8 = 72
72 = 72
3⁴y×2^x=2³×3²
2^x=2³
X=3
3⁴y=3²
y=2-¹
To find the values of x and y in the equation 9^(2y) * 2^x = 72, we can simplify the equation using the properties of exponents and logarithms.
First, we can rewrite 72 as 2^3 * 3^2, since 72 can be factored into 2 * 2 * 2 * 3 * 3.
So, our equation becomes:
9^(2y) * 2^x = 2^3 * 3^2
Next, we can simplify the equation further by using the rules of exponents. Since 9 is equal to 3^2, we can rewrite 9^(2y) as (3^2)^(2y), which simplifies to 3^(4y).
Now, our equation becomes:
3^(4y) * 2^x = 2^3 * 3^2
Since the bases of the exponents are the same (3 and 2), we can set the exponents equal to each other:
4y = 3 (equating the exponents of 3)
x = 3 (equating the exponents of 2)
Solving the equation 4y = 3 for y, we divide both sides by 4:
y = 3/4
So, the values of x and y in the equation 9^(2y) * 2^x = 72 are x = 3 and y = 3/4.