Final answer:
To express 2100 as an exponent with a base of 4, it can be approximated using logarithms to 4 to the power of approximately 7.177, as 2100 is not an exact power of 4.
Step-by-step explanation:
To write 2100 as an exponent with a base of 4, you need to find the power to which 4 must be raised to give the number 2100. This requires a bit of working with exponents. However, since 2100 isn't a power of 4, we need to use logarithms to express it as such:
2100 = 4^x
One way to solve for x is to take the logarithm of both sides of the equation, using a base of 4:
log42100 = x
You can use a calculator to determine this value, and you'll find:
x ≈ 7.177 (Note: The value is an approximation since 2100 is not an exact power of 4)
To write this as a single exponent with a base of 4, you can express the original number as:
2100 = 4^7.177
This equation may not satisfy the criteria for an integer exponent but it correctly represents 2100 using a base 4 exponent.