Problems 90-93 are based on material earlier in the course....

Problems $90-93$ are based on material earlier in the course. The purpose of these problems is to keep the material fresh in your. mind so that you are better prepared for the final exam.
$$
\text { Solve: } \log _{4}(x+3)-\log _{4}(x-1)=2
$$

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Key Concepts

Properties of Logarithms

This concept involves the rules that govern the operations on logarithms, such as the fact that the difference of two logarithms with the same base can be expressed as the logarithm of a quotient. For instance, the property log_a(M) - log_a(N) = log_a(M/N) is a crucial tool in simplifying and solving logarithmic expressions.

Solving Logarithmic Equations

This key concept focuses on the methods used to solve equations that contain logarithmic expressions. It often involves using logarithmic properties to combine or simplify terms and converting the logarithmic equation into an equivalent exponential form. This helps in isolating the variable and finding the solution.

Domain of Logarithmic Functions

Logarithmic functions are defined only for positive arguments. When solving logarithmic equations, it is essential to consider the domain restrictions to ensure that the solutions are valid. This involves ensuring that the expressions inside all logarithms are positive, which may restrict the possible values of the variable.

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