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.
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You're on a roll — Here are the solutions to the problems: 2.3.1. Solve for x: (3^x)(3^x-2) = 27 Step 1: Apply the exponent rule a^m · a^n = a^m+n on the left side and express the right side as a power of 3. 3^x + (x-2) = 3^3 3^2x-2 = 3^3 Step 2: Since the bases are equal, equate the exponents. 2x - 2 = 3 Step 3: Solve for x. 2x = 3 + 2 2x = 5 x = (5)/(2) The solution is x = (5)/(2). 2.3.2. Solve for x: -2x^2 + x = -3x(-2x+1) Step 1: Expand the right side of the equation. -2x^2 + x = (-3x)(-2x) + (-3x)(1) -2x^2 + x = 6x^2 - 3x Step 2: Move all terms to one side to form a standard quadratic equation. 0 = 6x^2 + 2x^2 - 3x - x 0 = 8x^2 - 4x Step 3: Factor out the common term. 0 = 4x(2x - 1) Step 4: Set each factor equal to zero and solve for x. 4x = 0 or 2x - 1 = 0 x = 0 or 2x = 1 x = 0 or x = (1)/(2) The solutions are x = 0 or x = (1)/(2). 2.4. Solve algebraically for x and y in the following equations: 1) 2x + 3y + 4 = 0 2) x + 2y - 5 = 0 Step 1: Isolate x from equation (2). x = -2y + 5 (Equation 3) Step 2: Substitute Equation 3 into Equation 1. 2(-2y + 5) + 3y + 4 = 0 Step 3: Simplify and solve for y. -4y + 10 + 3y + 4 = 0 -y + 14 = 0 -y = -14 y = 14 Step 4: Substitute the value of y back into Equation 3 to find x. x = -2(14) + 5 x = -28 + 5 x = -23 The solution is x = -23, y = 14. Send me the next one 📸