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Evaluating logarithms using properties involves applying key rules to simplify expressions: the Product Rule (\(\log_b(MN) = \log_b(M) + \log_b(N)\)), the Quotient Rule (\(\log_b\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N)\)), and the Power Rule (\(\log_b(M^k) = k \cdot \log_b(M)\)). These properties are effective only when the bases are the same. It facilitates breaking down complex logarithmic expressions into simpler, more manageable parts, making it easier to solve logarithmic equations and perform calculations.

Example: Simplify \(\log_2(8 \cdot 4) - \log_2(16) + \log_2(2^3)\).

Algebra 2

Logarithms