Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Evaluate the following expression without a calculator:

[tex]\(\log_4 256\)[/tex]

A. 4
B. 64
C. 16
D. 8

Sagot :

GinnyAnswer
To evaluate [tex]\( \log_4 256 \)[/tex], we need to determine the power to which the base 4 must be raised to obtain 256.

The expression [tex]\( \log_b(a) = c \)[/tex] means that [tex]\( b^c = a \)[/tex]. Therefore:
[tex]\[ \log_4(256) = x \][/tex]
implies
[tex]\[ 4^x = 256 \][/tex]

Next, we should recognize if 256 can be expressed as a power of 4. We proceed by determining the power relationship here:

[tex]\[ 4^1 = 4 \\ 4^2 = 16 \\ 4^3 = 64 \\ 4^4 = 256 \][/tex]

We see that:
[tex]\[ 256 = 4^4 \][/tex]

Therefore:
[tex]\[ 4^4 = 256 \][/tex]

This means:
[tex]\[ \log_4(256) = 4 \][/tex]

Thus, the correct answer is:

A. 4
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.