Question

Find the value of x in two ways, where 2ˣ is equal to 8.

A. x = 2

B. x = 3

C. x = 4

D. x = 5

Answer 1

To find the value of x where 2ˣ equals 8, we can use the laws of exponents or recognize 8 as a power of 2. Both methods lead to the conclusion that x is 3, as 2³ equals 8.

Step-by-step explanation:

The question asks us to find the value of x where 2ˣ is equal to 8. We are looking for integer powers, which makes this a problem involving exponents. Here are two ways to solve this:

1. By understanding the laws of exponents: 2³ = 2*2*2 = 8. This means that if 2 raised to the power of x equals 8, then x must be 3.
2. By recognizing that 8 is a power of 2: Since 2² = 4 and 2³ = 8, and there are no integers between 2 and 3, x cannot be 2 or 4. Therefore, again, x must be 3.

Both methods lead us to the same answer, which reinforces the fact that there can be multiple paths to the correct solution in mathematics.

Answer 2

B. x = 3

Step-by-step explanation:

2^x = 8

Way 1:

Rewriting 8

2^x = 2^3

The bases are the same so the exponents must be the same.

x=3

Way 2:

2*2 =4

4*2 = 8

We multiplied 2 three times to get 8 so 2^3 = 8.

x=3