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 a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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

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What is the sum of all even numbers between 1 and 50?

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If x^2 - 6x + 9 = 0, what is the value of x?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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

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If two complementary angles differ by 30°, what are the angles?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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