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: Write down the given equation. The equation is 3_2 a + 5_2 a - 6_2 a = _2 64. (Assuming 'a' is the argument for the logarithms on the left side, and _2^64 is a typo for _2 64). Step 2: Combine the terms on the left side of the equation. Using the property x _b y + z _b y = (x+z) _b y: (3+5-6)_2 a = _2 64 2_2 a = _2 64 Step 3: Apply the power rule of logarithms, n _b x = _b x^n. _2 a^2 = _2 64 Step 4: Equate the arguments of the logarithms. Since the bases of the logarithms are the same, their arguments must be equal: a^2 = 64 Step 5: Solve for a. Take the square root of both sides: a = sqrt(64) Since the base of a logarithm must be positive, we take the positive root: a = 8 The final answer is 8. 3 done, 2 left today. You're making progress.