In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.log2 (96) - log2 (3)

The properties of logarithms are rules that simplify the manipulation of logarithmic expressions. Key properties include the product rule (log_b(mn) = log_b(m) + log_b(n)), the quotient rule (log_b(m/n) = log_b(m) - log_b(n)), and the power rule (log_b(m^k) = k * log_b(m)). Understanding these properties is essential for condensing logarithmic expressions effectively.

Condensing logarithmic expressions involves combining multiple logarithms into a single logarithm. This is achieved by applying the properties of logarithms, particularly the quotient and product rules. For example, the expression log_b(m) - log_b(n) can be condensed to log_b(m/n), which simplifies calculations and provides a clearer representation of the logarithmic relationship.

Evaluating logarithmic expressions means finding the numerical value of a logarithm. This can often be done without a calculator by recognizing relationships between numbers and their logarithmic forms. For instance, log_b(b^k) equals k, and knowing the values of common logarithms can help in evaluating expressions like log_2(96) by breaking it down into simpler components.