To evaluate the expression (48.63 x 8.83)/(18.39 x 3.82) using logarithm tables, we will follow these steps:

To evaluate the expression (48.63 × 8.83)/(18.39 × 3.82) using logarithm tables, we will follow these steps: Let X = (48.63 × 8.83)/(18.39 × 3.82). Taking the logarithm of both sides: X = (48.63 × 8.83) - (18.39 × 3.82) Using the logarithm properties (ab) = a + b and ((a)/(b)) = a - b: X = ( 48.63 + 8.83) - ( 18.39 + 3.82) Step 1: Find the logarithms of each number using a 4-figure logarithm table. For 48.63: Characteristic: There are 2 digits before the decimal point, so the characteristic is 2-1=1. Mantissa: Look up 48 under 6, which is 6866. The mean difference for 3 is 3. So, 6866+3 = 6869. 48.63 = 1.6869 For 8.83: Characteristic: There is 1 digit before the decimal point, so the characteristic is 1-1=0. Mantissa: Look up 88 under 3, which is 9450. 8.83 = 0.9450 For 18.39: Characteristic: There are 2 digits before the decimal point, so the characteristic is 2-1=1. Mantissa: Look up 18 under 3, which is 2625. The mean difference for 9 is 21. So, 2625+21 = 2646. 18.39 = 1.2646 For 3.82: Characteristic: There is 1 digit before the decimal point, so the characteristic is 1-1=0. Mantissa: Look up 38 under 2, which is 5821. 3.82 = 0.5821 Step 2: Substitute the logarithm values into the equation for X. X = (1.6869 + 0.9450) - (1.2646 + 0.5821) Step 3: Perform the additions. Numerator sum: 1.6869 + 0.9450 = 2.6319 Denominator sum: 1.2646 + 0.5821 = 1.8467 Step 4: Perform the subtraction. X = 2.6319 - 1.8467 X = 0.7852 Step 5: Find the antilog of 0.7852. Mantissa: Look for 78 under 5 in the antilog table, which is 6095. The mean difference for 2 is 3. So, 6095+3 = 6098. Characteristic: The characteristic is 0. This means there is 0+1=1 digit before the decimal point. Antilog 0.7852 = 6.098 Therefore, X ≈ 6.098. (48.63 × 8.83)/(18.39 × 3.82) ≈ 6.098 3 done, 2 left today. You're making progress.