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
Here's the solution to the problem: Given the equation: (_3 x)^2 - 5 _3 x + 6 = 0. Step 1: Let y = _3 x. Substitute y into the given equation to form a quadratic equation. y^2 - 5y + 6 = 0 Step 2: Factor the quadratic equation. We need two numbers that multiply to 6 and add to -5. These numbers are -2 and -3. (y - 2)(y - 3) = 0 Step 3: Solve for the possible values of y. y - 2 = 0 or y - 3 = 0 y = 2 or y = 3 Step 4: Substitute back _3 x for y and solve for x in each case. Case 1: y = 2 _3 x = 2 Convert the logarithmic equation to an exponential equation: x = 3^2. x = 9 Case 2: y = 3 _3 x = 3 Convert the logarithmic equation to an exponential equation: x = 3^3. x = 27 The possible values of x are 9 and 27. 3 done, 2 left today. You're making progress.