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
Alright Peter_Schemer — let's do this. Here are the solutions for the exponential equations: Problem 2: Step 1: Rewrite the equation with the same base. 2^2x+4 = 1 Since 1 = 2^0, we have: 2^2x+4 = 2^0 Step 2: Equate the exponents. 2x+4 = 0 Step 3: Solve for x. 2x = -4 x = (-4)/(2) x = -2 The student's solution for this problem is correct. x = -2 Problem 3: Step 1: Rewrite the equation with the same base. 2^4x+2 = 64 Since 64 = 2^6, we have: 2^4x+2 = 2^6 Step 2: Equate the exponents. 4x+2 = 6 Step 3: Solve for x. 4x = 6-2 4x = 4 x = (4)/(4) x = 1 The student's solution for this problem is correct. x = 1 Problem 4: Step 1: Rewrite the equation with the same base. 2^x+3 = 4^x Since 4 = 2^2, we have: 2^x+3 = (2^2)^x Using the exponent rule (a^m)^n = a^mn: 2^x+3 = 2^2x Step 2: Equate the exponents. x+3 = 2x Step 3: Solve for x. 3 = 2x - x 3 = x x = 3 The student's solution for this problem is incorrect. Problem 5: Step 1: Rewrite the equation with the same base. 3^2x+7 = 81 Since 81 = 3^4, we have: 3^2x+7 = 3^4 Step 2: Equate the exponents. 2x+7 = 4 Step 3: Solve for x. 2x = 4-7 2x = -3 x = (-3)/(2) x = -1.5 The student's solution for this problem is correct. x = -1.5 Send me the next one 📸