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

What is the square root of 0.25?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the sum of all even numbers between 1 and 100?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If a number is divisible by 9, it is also divisible by which of the following?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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