step 1 This is problem number 26. We need to solve that is find the value of x for log x minus 5 to the

Solve log2|4-5 x|>2.

Name: Problem 6, Chapter 1: Mathematics for Joint Entrance Examination JEE (Advanced) Trigonometry
Uploaded: 2020-11-10T23:47:10-08:00
Duration: 43 s
Channel: Suman Saurav Thakur
Description: Solve log2|4-5 x|>2.

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Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions and are defined for positive arguments. They allow us to solve equations where the unknown appears in the exponent by converting between logarithmic and exponential forms, making them a fundamental tool in algebra and calculus.

Logarithmic Inequalities

Logarithmic inequalities involve solving for the variable within a logarithmic expression where an inequality sign is present. The solution process typically includes converting the inequality to an exponential form while carefully considering the monotonicity of the logarithm function, which depends on the base of the logarithm.

Absolute Value

The absolute value function measures the distance of a number from zero on the number line, irrespective of its sign. In equations or inequalities, incorporating absolute value leads to considering both the positive and negative scenarios of the expression wrapped by the absolute value.

Domain Restrictions for Logarithmic Functions

Since logarithms are only defined for positive arguments, any expression inside a logarithm must be set greater than zero. This requirement is critical when solving logarithmic equations or inequalities, as it ensures that the solution respects the inherent domain constraints.

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