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 1xbet, good to see you again. To find the value of x, we need to solve the given equation: 9sqrt(x) = sqrt(27^x) Step 1: Rewrite the numbers 9 and 27 as powers of 3, and express the square roots as fractional exponents. We know that 9 = 3^2 and 27 = 3^3. Also, sqrt(x) = x^1/2 and sqrt(27^x) = (27^x)^1/2. Substitute these into the equation: 3^2 · x^1/2 = ( (3^3)^x )^1/2