Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Logarithms
Understanding the properties of logarithms is essential for solving logarithmic equations. Key properties include the product rule, which states that log(a) + log(b) = log(ab), and the power rule, which allows for the manipulation of exponents within logarithms. These properties help simplify equations and combine logarithmic terms effectively.
Recommended video:
Solving Logarithmic Equations
To solve logarithmic equations, one typically isolates the logarithmic expression and then exponentiates to eliminate the logarithm. This process often involves rewriting the equation in exponential form, which can lead to a polynomial equation that can be solved using algebraic methods. It's crucial to check for extraneous solutions that may arise from the logarithmic properties.
Recommended video:
Solving Logarithmic Equations
Domain Restrictions of Logarithmic Functions
Logarithmic functions have specific domain restrictions, as the argument of a logarithm must be positive. In the equation log(x) + log(x - 21) = log(100), both x and (x - 21) must be greater than zero. This means x must be greater than 21, which is an important consideration when determining valid solutions to the equation.
Recommended video:
Domain Restrictions of Composed Functions