equivalent to log216

?

1 answer

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 \(4\).