Solve the Logarithm Expression: 2log₈2 + log₈3

This uses the power rule for logarithms: $n\log_a x = \log_a x^n$. So $2\log_82 = \log_8 2^2 = \log_8 4$. The coefficient becomes an exponent!

Key rule: When you add logarithms with the same base, you multiply their arguments: $\log_a x + \log_a y = \log_a(xy)$. Don't add the arguments - that's the most common mistake!

You cannot directly combine logarithms with different bases using these rules. You'd need to convert them to the same base first using the change of base formula: $\log_b x = \frac{\log_a x}{\log_a b}$.

Ask yourself: "What power of 8 gives me 12?" Since $8^1 = 8$ and $8^2 = 64$, the answer should be between 1 and 2. Also verify: $2^2 \cdot 3 = 4 \cdot 3 = 12$ ✓

That would be treating the logarithm expression like regular arithmetic! Remember, $\log_82$ is asking "what power of 8 gives 2?" - it's not equal to 2 itself. Always apply logarithm properties first.