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
Step 1: Rewrite the equation with a common base. The given equation is 4^3x+2 = 2^6x+2x. First, simplify the exponent on the right side: 4^3x+2 = 2^8x Since 4 = 2^2, substitute this into the equation: (2^2)^3x+2 = 2^8x Step 2: Apply the exponent rule (a^b)^c = a^bc. Multiply the exponents on the left side: 2^2(3x+2) = 2^8x 2^6x+4 = 2^8x Step 3: Equate the exponents. Since the bases are the same, the exponents must be equal: 6x+4 = 8x Step 4: Solve for x. Subtract 6x from both sides of the equation: 4 = 8x - 6x 4 = 2x Divide by 2: x = (4)/(2) x = 2 Comparing this result with the given options, x=2 corresponds to option D. The final answer is D. Send me the next one 📸