Final answer:
To solve the equation log3(1/9) = 2x - 1, rewrite it in exponential form and equate the exponents. The final answer is x = -1/2.
Step-by-step explanation:
To solve the equation log3(1/9) = 2x - 1, we need to isolate x. First, rewrite the equation in exponential form: 3^(2x-1) = 1/9. Since 1/9 can be written as 3^(-2), we have 3^(2x-1) = 3^(-2).
Since the bases are the same, the exponents must be equal. So, 2x - 1 = -2. Add 1 to both sides to isolate x and solve for x: 2x = -1. Add 1 to both sides to isolate x and solve for x: 2x = -1. Divide both sides by 2 to get the final answer: x = -1/2.