Topic Details (Notes format)

How to Solve Logarithmic Equations

Subject: Mathematics

Book: Maths Mastery

Logarithmic equations typically appear in forms like log_a(x) = b, which implies x = a^b. If you have log(2x – 1) = 2, you can rewrite it in exponential form as 2x – 1 = 10² = 100, yielding x = 50. More advanced problems might combine multiple log terms, requiring properties like log(mn) = log(m) + log(n) or log(m/n) = log(m) – log(n). Logarithms are crucial for measuring pH in chemistry, decibels in sound, or earthquake magnitudes on the Richter scale. Proficiency in solving log equations ensures the ability to tackle scientific data, high-level mathematics, and real-world measurement problems.

Practice Questions

What is the square root of 0.25?

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

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What is the LCM of 15 and 20?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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

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The area of an equilateral triangle with side length 6 cm is:

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

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If 5x - 2 = 13, what is the value of x?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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