The logarithm of 0.0625 to the base 2 is(a) 0.025(b) 0.25(c) 5(d) -4 (e) -2

To find the logarithm of 0.0625 to the base 2, you can use the following formula:

log₂(0.0625) = log(0.0625) / log(2)

First, calculate the numerator:

log(0.0625) = log(1/16)

Using the property that log(a/b) = log(a) - log(b), we get:

log(1/16) = log(1) - log(16) = 0 - log(16)

Now, calculate the denominator:

log(2) = This is the logarithm of 2 to the base 10, which is approximately 0.3010 (rounded to four decimal places).

Now, divide the numerator by the denominator:

log₂(0.0625) = (0 - log(16)) / 0.3010

Now, calculate:

log₂(0.0625) ≈ (-1.2041) / 0.3010 ≈ -4

So, the logarithm of 0.0625 to the base 2 is -4. Therefore, the correct answer is (d) -4.