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
Mukisa, let's knock this out. Step 1: Convert the first exponential equation to a linear equation. The given equation is 8^x = 4^(y+1). We can express both bases as powers of 2: 8 = 2^3 and 4 = 2^2. (2^3)^x = (2^2)^(y+1) Apply the power rule (a^m)^n = a^mn: 2^3x = 2^2(y+1) Since the bases are the same, the exponents must be equal: 3x = 2(y+1) 3x = 2y + 2 Rearrange to form a linear equation (Equation 1): 3x - 2y = 2 (1) Step 2: Convert the second exponential equation to a linear equation. The given equation is 3^(2x-y) = (1)/(27). We can express (1)/(27) as a power of 3: (1)/(27) = (1)/(3^3) = 3^-3. 3^(2x-y) = 3^-3 Since the bases are the same, the exponents must be equal: 2x - y = -3 (2) Step 3: Solve the system of linear equations. We have the system: 1) 3x - 2y = 2 2) 2x - y = -3 From Equation (2), we can express y in terms of x: y = 2x + 3 Substitute this expression for y into Equation (1): 3x - 2(2x + 3) = 2 3x - 4x - 6 = 2 -x - 6 = 2 -x = 2 + 6 -x = 8 x = -8 Now substitute the value of x back into the expression for y: y = 2(-8) + 3 y = -16 + 3 y = -13 The solution is x = -8 and y = -13. The final answer is x = -8, y = -13. Send me the next one 📸