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 LCM of 15 and 20?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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

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What is the square root of 0.25?

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

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If 2x = 16, what is the value of x?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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What is the remainder when 5^100 is divided by 3?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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