Topic Details (Notes format)

How to Solve Exponential Inequalities

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.

Practice Questions

A number is increased by 20% and then decreased by 10%. What is the net change?

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What is the value of log₃(27)?

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

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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What is the HCF of 72 and 120?

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A sphere has a radius of 7 cm. What is its volume?

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If the probability of an event is 1/4, what is the probability of its complement?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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