Topic Details (Notes format)

How to Solve Exponential Equations

Subject: Mathematics

Book: Maths Mastery

Exponential equations have the variable in the exponent, such as 2^x = 8. One approach is to rewrite both sides using the same base. For example, 8 can be written as 2³, so 2^x = 2³ implies x = 3. In more complicated cases, you may take logarithms of both sides: If 5^x = 100, applying log yields x log(5) = log(100), so x = log(100)/log(5). Exponential equations govern growth phenomena, from population expansions to radioactive decay, making them central in biology, finance (compound growth), and physics. Mastering exponential solving ensures you can interpret and forecast exponential trends accurately.

Practice Questions

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

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

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How many ways can 4 people sit in a row?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the value of log₃(27)?

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

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

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A cube has a side length of 4 cm. What is its volume?

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