Question
equivalent to log216
?
?
Answers
GPT-4o mini
To find an equivalent expression for \(\log_2 16\), we can use the fact that \(16\) can be expressed as a power of \(2\).
We know that:
\[
16 = 2^4
\]
Using the properties of logarithms, we can rewrite \(\log_2 16\) as follows:
\[
\log_2 16 = \log_2 (2^4)
\]
By applying the power rule of logarithms, which states that \(\log_b (a^c) = c \cdot \log_b a\), we have:
\[
\log_2 (2^4) = 4 \cdot \log_2 2
\]
Since \(\log_2 2 = 1\), this simplifies to:
\[
\log_2 16 = 4 \cdot 1 = 4
\]
Thus, \(\log_2 16\) is equivalent to \(4\).
We know that:
\[
16 = 2^4
\]
Using the properties of logarithms, we can rewrite \(\log_2 16\) as follows:
\[
\log_2 16 = \log_2 (2^4)
\]
By applying the power rule of logarithms, which states that \(\log_b (a^c) = c \cdot \log_b a\), we have:
\[
\log_2 (2^4) = 4 \cdot \log_2 2
\]
Since \(\log_2 2 = 1\), this simplifies to:
\[
\log_2 16 = 4 \cdot 1 = 4
\]
Thus, \(\log_2 16\) is equivalent to \(4\).