9^2y * 2^x = 72, find the value of x and y.

Not bad

To find the values of x and y in the equation 9^(2y) * 2^x = 72, we can start by simplifying the equation.

Step 1: Rewrite 72 as a product of prime numbers: 72 = 2^3 * 3^2.

Step 2: Rewrite 9^(2y) using exponent rules. Since 9 can be expressed as 3^2, we have (3^2)^(2y), which simplifies to 3^(4y).

Step 3: Substitute the values back into the equation: 3^(4y) * 2^x = 2^3 * 3^2.

Step 4: Rewrite the equation with all the same bases on one side: 3^(4y) * 2^x = 2^3 * 3^2.

Step 5: Using properties of exponents, equate the corresponding exponents: 4y = 3 and x = 3.

So, the values of x and y in the equation 9^(2y) * 2^x = 72 are x = 3 and y = 3/4.

by inspection:

9^1 * 2^3 = 72 , (9*8=72)
so 2y = 1 ---> y = 1/2
and 2^x = 2^3 ----> x = 3