Two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. If a= 32 , for what value of x is a x equal to b?
Question
Two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. If a= 32 , for what value of x is a x equal to b?
Solution
Given that a = 32 and 4√a = 9∛b, we can substitute a into the equation to find b.
Step 1: Substitute a into the equation 4√32 = 9∛b
Step 2: Simplify the left side of the equation 8 = 9∛b
Step 3: Solve for b b = (8/9)³ b = 512/729
Now, we need to find the value of x such that ax = b.
Step 4: Substitute a and b into the equation 32x = 512/729
Step 5: Solve for x x = (512/729) / 32 x = 16/729
So, the value of x for which ax = b is 16/729.
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