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 how to solve the exponential equation: 1.3.2 To solve 7^2x - 48(7^x) - 49 = 0, we can use a substitution to transform it into a quadratic equation. Step 1: Let u = 7^x. Then 7^2x = (7^x)^2 = u^2. Substitute u into the given equation: u^2 - 48u - 49 = 0 Step 2: Solve the quadratic equation for u. We can factor the quadratic expression: (u - 49)(u + 1) = 0 This gives two possible values for u: u = 49 or u = -1 Step 3: Substitute back 7^x for u and solve for x. Case 1: u = 49 7^x = 49 Since 49 = 7^2, we have: 7^x = 7^2 Therefore, x = 2. Case 2: u = -1 7^x = -1 An exponential function with a positive base (like 7) can never produce a negative result. Thus, there is no real solution for x in this case. The only valid solution for x is from Case 1. x = 2 3 done, 2 left today. You're making progress.