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
Hey master, good to see you again. Step 1: Rearrange the equation to isolate the term with x. We have the equation: (20)/((sqrt(2))^x) = (5)/(4) Multiply both sides by 4(sqrt(2))^x: 20 × 4 = 5 × (sqrt(2))^x 80 = 5 × (sqrt(2))^x Step 2: Divide both sides by 5. (80)/(5) = (sqrt(2))^x 16 = (sqrt(2))^x Step 3: Express both sides with the same base. We know that sqrt(2) = 2^1/2 and 16 = 2^4. Substitute these into the equation: 2^4 = (2^1/2)^x Using the exponent rule (a^m)^n = a^mn: 2^4 = 2^(x)/(2) Step 4: Equate the exponents. Since the bases are the same, the exponents must be equal: 4 = (x)/(2) Multiply both sides by 2 to solve for x: x = 4 × 2 x = 8 The value of x is 8. This corresponds to option (c). The final answer is c) 8. Send me the next one 📸