Final answer:
To solve 9^x = 3, rewrite 9 as 3^2, giving (3^2)^x = 3. By the power rule, 3^(2x) = 3^1, and equating exponents gives x = 1/2, which corresponds to Option 1.
Step-by-step explanation:
Finding the Value of x in 9^x = 3
To solve the equation 9^x = 3, we need to express both sides of the equation with the same base. Since 9 is 3 squared (3^2), we can rewrite the equation as (3^2)^x = 3. Applying the power rule of exponents, which states that (a^b)^c = a^(b*c), we get 3^(2x) = 3^1. Because the bases are now the same, the exponents must be equal for the equation to hold true, so 2x = 1. Dividing both sides by 2 gives us x = 1/2, which is Option 1.
This process demonstrates the use of exponent rules and understanding of fractional powers to solve equations involving exponents.