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
C) 2 Step 1: Evaluate the first logarithm term, ^64 256. We can express both the base and the argument as powers of 2. 64 = 2^6 and 256 = 2^8. Using the logarithm property _b^m a^n = (n)/(m) _b a: ^64 256 = _2^6 2^8 = (8)/(6) _2 2 Since _2 2 = 1: ^64 256 = (8)/(6) × 1 = (4)/(3) Step 2: Evaluate the second logarithm term, ^27 9. We can express both the base and the argument as powers of 3. 27 = 3^3 and 9 = 3^2. Using the logarithm property _b^m a^n = (n)/(m) _b a: ^27 9 = _3^3 3^2 = (2)/(3) _3 3 Since _3 3 = 1: ^27 9 = (2)/(3) × 1 = (2)/(3) Step 3: Add the results from Step 1 and Step 2. (4)/(3) + (2)/(3) = (4+2)/(3) = (6)/(3) = 2 The value of the expression is 2. Step 4: Compare the result with the given options. The calculated value is 2, which matches option C. The final answer is C) 2. Send me the next one 📸