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: Let the given expression be P. P = 3/(0.534) We can write this as: P = ((45.3 × 0.00697)/(0.534))^(1)/(3) Step 2: Take the logarithm of both sides. P = (((45.3 × 0.00697)/(0.534))^(1)/(3)) Using the logarithm property (a^b) = b a: P = (1)/(3) ((45.3 × 0.00697)/(0.534)) Using the logarithm properties ((a)/(b)) = a - b and (ab) = a + b: P = (1)/(3) [ (45.3) + (0.00697) - (0.534) ] Step 3: Find the logarithms of each number using a 4-figure logarithm table. • For (45.3): Characteristic: There are 2 digits before the decimal point, so the characteristic is 2-1=1. Mantissa: From log tables, the mantissa for 453 is 0.6561. So, (45.3) = 1.6561. • For (0.00697): Characteristic: The first non-zero digit (6) is in the third decimal place, so the characteristic is 3 (or -3). Mantissa: From log tables, the mantissa for 697 is 0.8432. So, (0.00697) = 3.8432. • For (0.534): Characteristic: The first non-zero digit (5) is in the first decimal place, so the characteristic is 1 (or -1). Mantissa: From log tables, the mantissa for 534 is 0.7275. So, (0.534) = 1.7275. Step 4: Substitute these values into the equation for P and perform the arithmetic. First, calculate the sum of the logarithms in the numerator: (45.3)