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
To evaluate the expression using logarithm tables, we first set the expression equal to N and then take the logarithm of both sides. Let N = 846.2 × sqrt(5436)[3]462.4. Step 1: Express the logarithm of N using logarithm properties. Using the properties (AB) = A + B, (A/B) = A - B, and (A^n) = n A: _10 N = _10(846.2) + _10(sqrt(5436)) - _10([3]462.4) _10 N = _10(846.2) + (1)/(2)_10(5436) - (1)/(3)_10(462.4) Step 2: Find the logarithm of each number. • For 846.2: The characteristic (integer part) is 3-1=2. The mantissa (decimal part) for 8462 from logarithm tables is approximately 0.9275. So, _10(846.2) = 2.9275. • For 5436: The characteristic is 4-1=3. The mantissa for 5436 from logarithm tables is approximately 0.7353. So, _10(5436) = 3.7353. • For 462.4: The characteristic is 3-1=2. The mantissa for 4624 from logarithm tables is approximately 0.6650. So, _10(462.4) = 2.6650. Step 3: Calculate the terms involving fractional exponents. (1)/(2)_10(5436) = (1)/(2) × 3.7353 = 1.86765 (1)/(3)_10(462.4) = (1)/(3) × 2.6650 = 0.88833... Step 4: Substitute these values back into the expression for _10 N and combine them. _10 N = 2.9275 + 1.86765 - 0.88833... First, add the positive terms: 2.9275 + 1.86765 = 4.79515 Now, subtract the negative term: _10 N = 4.79515 - 0.88833... = 3.906817... Rounding the mantissa to four decimal places for antilog table lookup: _10 N ≈ 3.9068 Step 5: Find the antilogarithm of 3.9068. The characteristic is 3, which means the number N will have 3+1=4 digits before the decimal point. The mantissa is 0.9068. Looking up 0.9068 in antilogarithm tables, we find the value is approximately 8.069. Therefore, N ≈ 8069. The evaluated expression is 8069. Last free one today — make it count tomorrow, or type /upgrade for unlimited.