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

If a:b = 5:7 and b:c = 6:11, what is a:c?

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If x - y = 5 and x + y = 15, what is the value of x?

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What is the sum of all odd numbers from 1 to 99?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If the radius of a circle is 7 cm, what is its circumference?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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What is the LCM of 15 and 20?

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What is the sum of the first 20 odd numbers?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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