What exponent would make the two expressions equivalent: (33)x=324?(1 point)

Question

Responses

21
21

15
15

27
27

8

Answer 1

Let's analyze the problem step by step:

We have the equation (33)^x = 324.

To find the exponent that would make the two expressions equivalent, we need to write both sides with the same base.

We can rewrite 324 as a power of 3 since 3^4 = 81 and 3^4 x 4 = 324:

324 = 3^4 x 4

Now, let's rewrite the equation:

(33)^x = 3^4 x 4

To make the bases the same, we need to rewrite 33 as a power of 3. Since 3^2 = 9, we can rewrite 33 as (3^2)^x:

(3^2)^x = 3^4 x 4

Now, we can simplify the equation by using the power of a power property:

3^(2x) = 3^4 x 4

Since the bases are the same on both sides, we can equate the exponents:

2x = 4

Dividing both sides by 2 gives us:

x = 2

Therefore, the exponent that would make the two expressions equivalent is 2.