Using the change of base formula, express $$ \log_{2}(8) $$ in terms of common logarithm.

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To express $$ \log_{2}(8) $$ in terms of common logarithm (base 10), we can use the change of base formula, which states:

$$
\log_{b}(a) = \frac{\log_{c}(a)}{\log_{c}(b)}
$$

where $$ b $$ is the base we want to change from, $$ a $$ is the argument of the logarithm, and $$ c $$ is the new base we want to use (in this case, base 10).

For $$ \log_{2}(8) $$, we can apply the change of base formula as follows:

$$
\log_{2}(8) = \frac{\log_{10}(8)}{\log_{10}(2)}
$$

Next, we can calculate $$ \log_{10}(8) $$ and $$ \log_{10}(2) $$ using their known values or approximations. However, we can also express $$ 8 $$ as a power of $$ 2 $$:

$$
8 = 2^3
$$

Thus, we can rewrite $$ \log_{2}(8) $$ as:

$$
\log_{2}(8) = \log_{2}(2^3) = 3
$$

Now, substituting back into the change of base formula, we have:

$$
\log_{2}(8) = \frac{\log_{10}(8)}{\log_{10}(2)} = 3
$$

This confirms that:

$$
\log_{2}(8) = 3
$$

In terms of common logarithm, we can express it as:

$$
\log_{2}(8) = \frac{\log_{10}(8)}{\log_{10}(2)} = 3
$$

Thus, the final answer is:

$$
\log_{2}(8) = \frac{\log_{10}(8)}{\log_{10}(2)}
$$
$$\log_{2}(8) = \frac{\log_{10}(8)}{\log_{10}(2)}$$

Using the change of base formula, express in terms of common logarithm.

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