Logarithmic Equations
This page focuses on equazioni logaritmiche logarithmicequations and provides methods for solving them. It offers logaritmi esercizi svolti facili easysolvedlogarithmexercises to illustrate the concepts.
The general form of a simple logarithmic equation is presented:
Definition: log_af(x) = k, where a > 0, a ≠ 1, and k is a real number
The solution process typically involves the following steps:
- Check the domain argumentmustbepositive
- Apply the definition of logarithms: if log_af(x) = k, then a^k = fx
- Solve the resulting equation for x
Example: Solve log_2x−4 = 0
Solution: 2^0 = x - 4, so x = 5
The page emphasizes the importance of checking the domain and verifying solutions:
Highlight: Always check the domain condition fx > 0 and verify that the solutions satisfy this condition.
More complex equations involving multiple logarithms or other functions are also discussed. These often require additional algebraic manipulation or the use of logarithm properties.
Example: Solve log_2x2−3 = -1
Solution: x^2 - 3 = 2^−1 = 1/2, so x^2 = 7/2, and x = ±√7/2
Understanding these techniques is crucial for solving more advanced problems involving logaritmi esercizi con soluzioni logarithmexerciseswithsolutions.