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
You're on a roll — Step 1: Let the given expression be Y. Y = 3^2)/(185.4) Rewrite the cube root as an exponent: Y = ((36.72 × (0.46)^2)/(185.4))^(1)/(3) Step 2: Take the logarithm (base 10) of both sides. Y = (((36.72 × (0.46)^2)/(185.4))^(1)/(3)) Apply the logarithm rule (A^B) = B A: Y = (1)/(3) ((36.72 × (0.46)^2)/(185.4)) Apply the logarithm rules ((A)/(B)) = A - B and (AB) = A + B: Y = (1)/(3) ( (36.72) + ((0.46)^2) - (185.4) ) Apply the logarithm rule (A^B) = B A again: Y = (1)/(3) ( (36.72) + 2 (0.46) - (185.4) ) Step 3: Find the logarithms of each number using logarithm tables. • For (36.72): Characteristic: 1 (since 36.72 has two digits before the decimal point, 2-1=1). Mantissa: Look up 36 under 7 (which is 0.5647) and mean difference for 2 (which is 2). So, (36.72) = 1.5647 + 0.0002 = 1.5649. • For (0.46): Characteristic: 1 (since the first significant digit is in the first decimal place). Mantissa: Look up 46 under 0 (which is 0.6628). So, (0.46) = 1.6628. • For (185.4): Characteristic: 2 (since 185.4 has three digits before the decimal point, 3-1=2). Mantissa: Look up $