If log3x2 = -8, what is x?

We can start by using the definition of logarithms to rewrite the equation: log3(x^2) = -8 This means that 3 raised to the power of -8 is equal to x^2: 3^(-8) = x^2 To solve for x, we can take the square root of both sides: sqrt(3^(-8)) = sqrt(x^2) On the left side, we can simplify the expression using the rule that says sqrt(a^b) = a^(b/2): 3^(-8/2) = x Simplifying the exponent, we get: 3^(-4) = x Recall that a negative exponent means the reciprocal of the corresponding positive exponent. So: 3^(-4) = 1/3^4 Using the exponent rule that says a^b = a*a*a*...*a (b times), we get: 1/81 = x Therefore, the correct answer is option (D) 181.