Question 3 (1 point) Solve for the missing information: $$ \log _{4}(64)=? ? ? $$ 2 3 16 Not enough information to solve.

Question

UpStudy AI · Accepted Answer

To solve for $$ \log_{4}(64) $$, we need to determine what power we must raise 4 to in order to get 64.

We can express 64 as a power of 4. First, let's rewrite 64 in terms of base 4:

$$
64 = 4^3
$$

Now, we can set up the logarithmic equation:

$$
\log_{4}(64) = \log_{4}(4^3)
$$

Using the property of logarithms that states $$ \log_{b}(b^x) = x $$, we can simplify this:

$$
\log_{4}(4^3) = 3
$$

Thus, the answer is:

$$
\log_{4}(64) = 3
$$

So the correct answer is **3**.
$$ \log_{4}(64) = 3 $$

Question 3 (1 point) Solve for the missing information: \( \log _{4}(64)=? ? ? \) 2 3 16 Not enough information to solve.