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 vukona — missed you this week. Here are the solutions to the exponential equations: a) Solve 8^x = (1)/(4) Step 1: Express both sides with the same base. (2^3)^x = 2^-2 Step 2: Simplify the exponent on the left side. 2^3x = 2^-2 Step 3: Equate the exponents and solve for x. 3x = -2 x = -(2)/(3) The solution is x = -(2)/(3). b) Solve 5^x+1 = 125 Step 1: Express both sides with the same base. 5^x+1 = 5^3 Step 2: Equate the exponents and solve for x. x+1 = 3 x = 3-1 x = 2 The solution is x = 2. c) Solve 3^2x-1 = (1)/(27) Step 1: Express both sides with the same base. 3^2x-1 = 3^-3 Step 2: Equate the exponents and solve for x. 2x-1 = -3 2x = -3+1 2x = -2 x = -1 The solution is x = -1. d) Solve 2^x+2 = 6 Step 1: Take the logarithm of both sides. Using _2 is convenient here. _2(2^x+2) = _2(6) Step 2: Use the logarithm property _b(b^y) = y. x+2 = _2(6) Step 3: Solve for x. x = _2(6) - 2 The solution is x = _2(6) - 2. e) Solve 3^x-3 = 6 Step 1: Take the logarithm of both sides. Using _3 is convenient here. _3(3^x-3) = _3(6) Step 2: Use the logarithm property _b(b^y) = y. x-3 = _3(6) Step 3: Solve for x. x = _3(6) + 3 The solution is x = _3(6) + 3. Send me the next one 📸