Write 2^100 as a power with the following base.
16
2^100 can be written as (2^4)^(100/4) since 16 is equal to 2^4.
Therefore, 2^100 can also be written as 16^(100/4).
Simplifying, we get 16^25 as the power with base 16.
To write 2^100 as a power with the base of 16, we first need to find the logarithm of 2 with base 16.
Let's set up the equation:
16^x = 2
Taking the logarithm of both sides using base 16:
log16(16^x) = log16(2)
Simplifying the equation further:
x = log16(2)
Now, we can calculate the value of x:
x ≈ 0.25
Therefore, 2^100 can be written as 16^(0.25 * 100).