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
Welcome back shine — missed you this week. Step 1: Apply the logarithm property _b x - _b y = _b ((x)/(y)) to the first two terms. _8 2 - _8 0.25 + _8 32 = _8 ((2)/(0.25)) + _8 32 Step 2: Simplify the argument of the first logarithm. _8 ((2)/(0.25)) = _8 ((2)/(1)4) = _8 (2 × 4) = _8 8 The expression becomes: _8 8 + _8 32 Step 3: Apply the logarithm property _b x + _b y = _b (x · y) to the remaining terms. _8 8 + _8 32 = _8 (8 × 32) Step 4: Simplify the argument of the logarithm. _8 (8 × 32) = _8 256 Step 5: Evaluate the logarithm. Let x = _8 256. This means 8^x = 256. We can express both 8 and 256 as powers of 2: 8 = 2^3 256 = 2^8 Substitute these into the equation: (2^3)^x = 2^8 2^3x = 2^8 Equating the exponents: 3x = 8 x = (8)/(3) The final answer is (8)/(3). Send me the next one 📸