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To identify properties of logarithms given an equation, look for ways to apply logarithmic rules such as the product rule \(\log_b(xy) = \log_b(x) + \log_b(y)\), the quotient rule `\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)`, and the power rule \(\log_b(x^k) = k \log_b(x)\). Recognizing these properties allows us to simplify and solve logarithmic equations more effectively.

Example: Given the equation \(\log_b(x^2) = 2 \log_b(x)\), identify the logarithmic property used.

Algebra 2

Logarithms