Subject: Mathematics
Book: Maths Mastery
Exponential inequalities, like 2^x > 10 or 3^(x–1) ≤ 27, often require taking logarithms or rewriting terms. For 2^x > 10, x>log₂(10), so x> ~3.3219. Alternatively, if 3^(x–1)≤27, note 27=3³, so x–1≤3 → x≤4. Watch for sign flips if the base is between 0 and 1 (like (1/2)^x). These inequalities apply to population bounds, decay processes, or resource management. Mastering exponential inequalities fosters confident handling of wide-ranging growth/decay constraints in scientific, financial, or engineering domains.
If a+b = 10 and ab = 21, what is the value of a^3 + b^3?
View QuestionWhat is the slope of a line passing through the points (2, 3) and (4, 7)?
View QuestionIf 2x = 16, what is the value of x?
View QuestionA number is increased by 20% and then decreased by 10%. What is the net change?
View QuestionIf the sum of the squares of two consecutive positive integers is 365, what are the integers?
View QuestionA rectangle has an area of 48 cm² and a length of 8 cm. What is its width?
View QuestionWhat is the cube of 4?
View QuestionA train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?
View QuestionWhat is the square root of 144?
View QuestionWhat is the HCF of 72 and 120?
View Question