Topic Details (Notes format)

How to Solve Logarithmic Inequalities

Subject: Mathematics

Book: Maths Mastery

Log inequalities like log(x) > 2 or log₂(x–1) ≤ 3 require understanding domain (x>0 for log base 10, x–1>0 for log₂) and exponential transformations. For log(x)>2, rewrite as x>10²=100. Solve carefully, checking intervals against log domain constraints. More complex expressions may involve combining log properties or adding constants. Log inequalities arise in pH ranges, decibel thresholds, or exponential growth constraints. Systematic approach ensures correct intervals, avoiding extraneous solutions from domain missteps.

Practice Questions

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

View Question

What is the sum of all even numbers between 1 and 100?

View Question

The probability of getting an even number when rolling a die is:

View Question

If the perimeter of a square is 40 cm, what is the area of the square?

View Question

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

View Question

If the perimeter of a square is 36 cm, what is the length of its diagonal?

View Question

If a:b = 7:9 and b:c = 5:6, what is a:c?

View Question

What is the HCF of 48 and 180?

View Question

If a = 4 and b = 5, what is the value of (a+b)^2?

View Question

If the sum of the squares of two consecutive positive integers is 365, what are the integers?

View Question