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
3. Solve for x: 3^x = 81 Step 1: Express 81 as a power of 3. 81 = 3 × 3 × 3 × 3 = 3^4 Step 2: Substitute this into the equation. 3^x = 3^4 Step 3: Since the bases are the same, equate the exponents. x = 4 The value of x is 4. 4. Find the square root of 64. Step 1: Find a number that, when multiplied by itself, equals 64. 8 × 8 = 64 Step 2: Therefore, the square root of 64 is 8. sqrt(64) = 8 The square root of 64 is 8. 5. Find the square root of (16)/(25). Step 1: Apply the property of square roots for fractions: sqrt((a)/(b)) = sqrt(a)sqrt(b). sqrt((16)/(25)) = sqrt(16)sqrt(25) Step 2: Find the square root of the numerator (16). sqrt(16) = 4 Step 3: Find the square root of the denominator (25). sqrt(25) = 5 Step 4: Combine the results. sqrt(16)sqrt(25) = (4)/(5) The square root is (4)/(5). 6. Without dividing, show that 5346 is divisible by 9. Step 1: Recall the divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Step 2: Calculate the sum of the digits of 5346. 5 + 3 + 4 + 6 = 18 Step 3: Check if the sum of the digits (18) is divisible by 9. 18 ÷ 9 = 2 Since 18 is divisible by 9, the number 5346 is also divisible by 9. Therefore, 5346 is divisible by 9. 3 done, 2 left today. You're making progress.