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

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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If 2x - 3 = 7, what is the value of x?

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What is the cube root of 729?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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If x - y = 5 and x + y = 15, what is the value of x?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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