Question

What value of n makes the equation true? 2^n = 1024
a) 2
b) 10
c) 30
d) 1

Answer 1

To determine which value of n makes the equation 2^n = 1024 true, we can list the powers of 2 until we reach 1024, which is 2^10. Therefore, the correct value of n is 10.

Step-by-step explanation:

To find the value of n that makes the equation 2^n = 1024 true, we must recognize that 1024 is a power of 2. By knowing our powers of 2, we can determine that:

• 2^1 = 2
• 2^2 = 4
• 2^3 = 8
• 2^4 = 16
• 2^5 = 32
• 2^6 = 64
• 2^7 = 128
• 2^8 = 256
• 2^9 = 512
• 2^10 = 1024

So, the value of n that makes the equation true is 10.

This exercise touches upon concepts of exponents and scientific notation as well, which are fundamental in understanding how large numbers can be expressed compactly, as seen in various scientific and mathematical contexts, such as the growth of cells or when working with large multipliers like 10^2.