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 2a + b = 10 and a - b = 4, what is the value of a?

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The probability of rolling a sum of 7 with two dice is:

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What is the LCM of 15 and 20?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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A car travels 240 km in 4 hours. What is its average speed?

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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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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If the radius of a circle is doubled, what happens to its area?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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