Logarithm rules. Game on.

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

The product rule rewrites a sum of logs as a log of a product, so $\log 2 + \log 5 = \log(2\cdot 5)\textsf{.}$

$\log a + \log b = \log(ab)$ is the product rule.

$5^{2} = 25$, so $\log_{5}(25) = 2$.

The product rule rewrites a log of a product as a sum of logs, so $\log(3\cdot 4) = \log 3 + \log 4\textsf{.}$

$3\log a = \log(a^{3})$ is the power rule.

$2^{4} = 16$, so $\log_{2}(16) = 4$.

The power rule rewrites a coefficient on a log as an exponent on the argument, so $4\log 3 = \log(3^{4})\textsf{.}$