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.