Question

Select the correct answer. what is the solution to this equation? 3^2x = 1/3

Answer 1

x= 1/27

Explanation:

the correct answer is : X = 1/27

Answer 2

- 1/2

Explanation:

To solve for x in the equation 3^2x = 1/3, we can start by taking the logarithm of both sides with base 3:

log3 (3^2x) = log3 (1/3)

Using the logarithmic property logb (a^n) = n * logb (a), we can simplify the left side:

2x * log3 (3) = log3 (1/3)

Since log3 (3) = 1, we can simplify further:

2x = log3 (1/3)

To find the value of the logarithm on the right side, we can use the definition of logarithms: logb (a) = c if and only if b^c = a. Since 1/3 = 3^-1, we have:

2x = log3 (3^-1) = -1

Finally, to solve for x, we divide both sides of the equation by 2:

x = -1/2

So the solution to the equation 3^2x = 1/3 is x = -1/2.