The function 𝑓 is given by 𝑓𝑥=log2𝑥. What input value in the domain of 𝑓 yields an output value of 4 ?

1. Break Down the Problem

We need to find the input value $x$ such that $f(x) = 4$. The function is given as $f(x) = \log_2 x$. Therefore, we need to solve the equation:

$\log_2 x = 4$

2. Relevant Concepts

To solve for $x$, we can use the property of logarithms which states:

$\log_b a = c \implies a = b^c$

In this case, $b = 2$, $a = x$, and $c = 4$.

3. Analysis and Detail

Using the logarithmic property, we rewrite the equation:

$x = 2^4$

Now we perform the calculation for $2^4$:

$2^4 = 16$

4. Verify and Summarize

Thus, the input value that we are looking for is $x = 16$.

Final Answer

The input value in the domain of $f$ that yields an output value of 4 is $x = 16$.