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: Start with the given equation. sqrt((8^x)/(2^x)) = 4 Step 2: Square both sides of the equation to eliminate the square root. (sqrt((8^x)/(2^x)))^2 = 4^2 (8^x)/(2^x) = 16 Step 3: Rewrite the bases 8 and 16 as powers of 2. ((2^3)^x)/(2^x) = 2^4 Step 4: Apply the exponent rule (a^m)^n = a^mn to the numerator. 2^3x2^x = 2^4 Step 5: Apply the exponent rule (a^m)/(a^n) = a^m-n to the left side. 2^3x-x = 2^4 2^2x = 2^4 Step 6: Since the bases are equal, equate the exponents. 2x = 4 Step 7: Solve for x by dividing both sides by 2. x = (4)/(2) x = 2 The final answer is 2. 3 done, 2 left today. You're making progress.