step 1 To solve the given equation, the given equation is law base 3 of x equal to 2. We know that law

Solve log3|x|>2. | Numerade

Name: Problem 1, Chapter 1: Mathematics for Joint Entrance Examination JEE (Advanced) Trigonometry
Uploaded: 2020-05-17T18:29:12-08:00
Duration: 29 s
Channel: Jeyasree R T
Description: Solve log3|x|>2.

Key Concepts

Inequality Solving Techniques

Solving inequalities, as opposed to equations, requires special attention to the direction of the inequality sign, especially when applying transformations to both sides of the inequality. It is important to maintain the correct direction when dealing with monotonically increasing functions like logarithms with a base greater than one, ensuring that the steps in the solution preserve the inequality's validity.

Absolute Value

The absolute value function measures the distance of a number from zero on the number line, regardless of its sign. When a logarithm involves an absolute value, it means that both positive and negative inputs, provided they satisfy the magnitude condition, are considered. This ensures that the domain of the function is correctly handled and that the complete solution set is found.

Conversion Between Logarithmic and Exponential Forms

When faced with a logarithmic inequality, converting it to its exponential form simplifies the process of finding the solution. The conversion is based on the equivalence stating that if log_b(y) > k (with b > 1), then y > b^k. This process is essential in isolating the variable and solving the inequality.

Logarithmic Functions

Logarithms are the inverse operations of exponentiation. Understanding that a logarithm answers the question 'to what exponent must the base be raised to yield a given number' is critical. This concept allows one to translate between the logarithmic and exponential forms, which is especially useful in solving equations or inequalities containing logarithms.

Please give Ace some feedback