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

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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What is the value of x if 3x + 7 = 16?

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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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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What is the greatest common divisor (GCD) of 36 and 48?

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

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

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