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 Nuguse — missed you this week. The equation from the image is: 5^2(x+3) = 7^x+3 Step 1: Take the natural logarithm of both sides of the equation. (5^2(x+3)) = (7^x+3) Step 2: Use the logarithm property (a^b) = b (a) to bring the exponents down. 2(x+3)(5) = (x+3)(7) Step 3: Move all terms to one side of the equation. 2(x+3)(5) - (x+3)(7) = 0 Step 4: Factor out the common term (x+3). (x+3)(2(5) - (7)) = 0 Step 5: For the product of two factors to be zero, at least one of the factors must be zero. We have two possibilities: Possibility 1: x+3 = 0 x = -3 Possibility 2: 2(5) - (7) = 0 This simplifies to (5^2) = (7), which means (25) = (7). Since 25 ≠ 7, this statement is false, and this factor cannot be zero. Therefore, the only valid solution is from Possibility 1. The solution is: x = -3 Send me the next one 📸