![In the given grid, find the missing number: [32, 8; 128, ?]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777273683680-dc410cb1e73710dd.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Express the given numbers as powers of a common base. The numbers in the grid are 32, 8, and 128. These can all be expressed as powers of 2. 32 = 2^5 \\ 8 = 2^3 \\ 128 = 2^7 Let the missing number be X. We assume X is also a power of 2, so X = 2^x. Step 2: Form a grid of the exponents. The grid of numbers is: 32 & 8 \\ 128 & ? Replacing the numbers with their exponents (base 2): 5 & 3 \\ 7 & x Step 3: Identify the pattern in the exponents. Observe the sum of the exponents in the first row: 5 + 3 = 8 Assume the same pattern applies to the second row, meaning the sum of the exponents in the second row is also 8. 7 + x = 8 Step 4: Solve for the missing exponent x. x = 8 - 7 \\ x = 1 Step 5: Calculate the missing number X. Since X = 2^x and x = 1: X = 2^1 \\ X = 2 Step 6: Compare the result with the given options. The calculated missing number is 2. The options are: A. 4 B. 3 C. 6 D. 2 E. 8 The calculated value matches option D. The final answer is D. 2. 2 done, 3 left today. You're making progress.