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

Ask by Riley Norris. in the United States
Feb 21,2025

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Answer

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

Solution

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**.

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Beyond the Answer

To solve \( \log _{4}(64) \), we need to express 64 as a power of 4. Since \( 4^3 = 64 \), it follows that \( \log _{4}(64) = 3 \). So the answer is 3! Next, did you know that logarithms have been around since the early 17th century? They were invented to simplify complex calculations, especially for astronomers. John Napier came up with this fantastic idea to help multiply and divide large numbers by transforming them into addition and subtraction! If you find logarithms tricky, here's a quick tip: Always convert between bases! If you're stuck, try writing the equation in exponential form. Remember, \( \log_{b}(a) = c \) translates to \( b^c = a \)! It's a neat little trick that can save you a lot of time and confusion.

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