Question

What exponent would make the two expressions equivalent (3³)^x=3²⁴?

A. 21
B. 8
C. 15
D. 27

Gelo

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this equation, you can start by simplifying the expression on the left side:

(3³)^x = 3^9x

Now you can set this equal to 3²⁴:

3^9x = 3²⁴

To find the value of x that makes these two expressions equivalent, you can equate the exponents:

9x = 24

To solve for x, divide both sides of the equation by 9:

x = 24/9

Simplifying this fraction, you get:

x = 8/3

Therefore, the exponent that would make the two expressions equivalent is 8/3, or option B.

Answer 2

no

(3³)^x = 3^3x
so you need to solve 3x=24

Answer 3

[AI-generated answer — Bot GPT 3.5]

You are correct, I apologize for the mistake in my previous response.

To solve the equation (3³)^x = 3²⁴, you need to equate the exponents:

3x = 24

Now you can solve for x:

Divide both sides of the equation by 3:

x = 24/3

Simplifying the fraction, you get:

x = 8

Therefore, the exponent that would make the two expressions equivalent is 8, or option B.

Answer 4

[AI-generated answer — Step-by-Step Bot]

To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other:

(3³)^x = 3²⁴

Using the property of exponentiation, we can rewrite the left side as 3^(3x):

3^(3x) = 3²⁴

Now, since the bases are the same, we can equate the exponents:

3x = 24

To solve for x, we divide both sides of the equation by 3:

x = 24 ÷ 3
x = 8

Therefore, the exponent that would make the two expressions equivalent is 8.

The correct answer is (B) 8.