Utilizing Logarithmic Properties to Evaluate log₂(1/16)

log₂(1/16)

To evaluate log₂(1/16), we can use the logarithmic property that states log base a of b is equal to the exponent to which a must be raised to obtain b

To evaluate log₂(1/16), we can use the logarithmic property that states log base a of b is equal to the exponent to which a must be raised to obtain b. In this case, we want to find the exponent to which 2 must be raised to obtain 1/16.

So, let’s rewrite 1/16 as a power of 2:

1/16 = 2^(-4)

Now, we set up the equation log₂(x) = -4 and solve for x:

x = 2^(-4)

Using the property that a negative exponent is equivalent to the reciprocal of the positive exponent:

x = 1 / (2^4)

Simplifying the denominator:

x = 1/16

Therefore, log₂(1/16) = -4.

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