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

View Question

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

View Question

A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

View Question

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

View Question

If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

View Question

If 2a + b = 10 and a - b = 4, what is the value of a?

View Question

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

View Question

What is the LCM of 15 and 20?

View Question

What is the HCF of 48 and 180?

View Question

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

View Question