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. Use logarithms only to evaluate, correct to 4 decimal places: ((12.78 33.45^)/((9.063)^2))^1/3 Let X = ((12.78 33.45^)/((9.063)^2))^1/3. Taking logarithms to base 10: X = (1)/(3) ( (12.78) + ( 33.45^) - 2 (9.063) ) Step 1: Find the logarithm of each term. Using logarithm tables: (12.78) = 1.1065 33.45^ = 0.5512 ( 33.45^) = (0.5512) = 1.7413 (9.063) = 0.9572 Step 2: Substitute the logarithm values into the equation for X. X = (1)/(3) (1.1065 + 1.7413 - 2 × 0.9572) X = (1)/(3) (1.1065 + (-1 + 0.7413) - 1.9144) X = (1)/(3) (1.1065 - 0.2587 - 1.9144) X = (1)/(3) (0.8478 - 1.9144) X = (1)/(3) (-1.0666) Step 3: Divide by 3. X = -0.355533... Step 4: Convert the negative logarithm to characteristic-mantissa form. -0.3555 = -1 + 0.6445 So, $ X = 1.6