Questions: Evaluate the log base 2 of 1/16. Write your answer in simplest form.

Transcript text: Evaluate the $\log _{2} \frac{1}{16}$. Write your answer in simplest form.

Solution

Step 1: Convert the logarithm of a fraction into the logarithm of a power

Given the expression $\log_{2}\left(\frac{1}{2^4}\right)$, we can use the property $\log_{2}(a^{-n}) = -n \cdot \log_{2}(a)$.

Step 2: Apply the change of base formula if necessary

Since $b$ is equal to $a$, the logarithm simplifies directly without needing the change of base formula.

Step 3: Simplify the expression

Since $b = a$, $\log_{2}(2) = 1$, thus the expression simplifies to $-n = -4$.

The value of $\log_{2}\left(\frac{1}{2^4}\right)$ is approximately $-4$, rounded to 0 decimal places.

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