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: Use the logarithm properties a + b = (ab) and a - b = ((a)/(b)) to combine the terms. 162 + 36 - 54 = ((162 × 36)/(54)) Step 2: Simplify the expression inside the logarithm. (162 × 36)/(54) = (162)/(54) × 36 = 3 × 36 = 108 So the expression becomes: 108 Step 3: Express 108 as a product of powers of 2 and 3, since we are given 2 and 3. 108 = 2 × 54 = 2 × 2 × 27 = 2^2 × 3^3 Step 4: Substitute this back into the logarithm and use the properties (ab) = a + b and a^n = n a. 108 = (2^2 × 3^3) = 2^2 + 3^3 = 2 2 + 3 3 Step 5: Substitute the given values 2 = 0.3010 and 3 = 0.4771. 2(0.3010) + 3(0.4771) Step 6: Perform the multiplication and addition. 0.6020 + 1.4313 = 2.0333 The evaluated expression is: 2.0333 Send me the next one 📸