If 3\(^{2x}\) = 27, what is x?

We can solve for x by using the laws of exponents and taking the logarithm of both sides. First, we can rewrite 3²x as (3²)ⁿ, where n = 2x. So, we have: (3²)ⁿ = 27 3ⁿ² = 27 Now, we can take the logarithm of both sides of the equation. Let's use the natural logarithm, denoted as ln, which is the logarithm to the base e: ln(3ⁿ²) = ln(27) Using the power rule of logarithms, we can simplify the left-hand side: n² ln(3) = ln(27) Now, we can solve for n: n² = ln(27) / ln(3) n² = 3 Taking the square root of both sides, we get: n = ± √3 But we know that n = 2x, so we can substitute back: 2x = ± √3 Solving for x, we get: x = ± (1/2) √3 Since the question is asking for a real value of x, we can take the positive square root: x = (1/2) √3 ≈ 0.866 Therefore, x is approximately 0.866, which is option (B) 1.5 rounded to one decimal place.