## JEE Advanced Maths Logarithm Important Questions from PYQs with Solutions

## FAQs on JEE Advanced Logarithms Important Questions

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6. What are the rules when adding logs?

You can only add logs if they have the same base. When adding logs with the same base, you multiply the numbers inside the logs (arguments).

7. When adding logs do you multiply?

Yes, adding logs with the same base is done by multiplying the arguments.

8. What are the 7 rules of logarithms?

There are several important rules of logarithms, but common ones include:

Product Rule: $\log_b(mn) = \log_b(m) + \log_b(n)$ (log of a product equals the sum of logs of factors)

Quotient Rule: $\log_b \left(\dfrac{m}{n}\right) = \log_b(m) - \log_b(n)$ (log of a quotient equals log of numerator minus log of denominator)

Power Rule: $\log_b(m^n) = n \log_b(m)$ (log of an exponent equals exponent times log of base)

9. How do you cancel logarithms?

You can only cancel logarithms if they have the same argument (the number inside the log) AND the same base.

10. When two logs are divided?

Dividing logs with the same base is the same as subtracting their arguments. So, $\dfrac{\log_b(m)}{\log_b(n)}$ is equal to $\log_b(m) - \log_b(n)$.

11. How do you expand logs?

Logarithms can sometimes be expanded using the product and quotient rules. For instance, log(xy) can be expanded to log(x) + log(y).

12. Who invented logarithm?

John Napier, a Scottish mathematician, is generally credited with inventing logarithms in the early 17th century.

13. Why is logarithm used?

Logarithms are useful in many fields because they can compress large numbers into smaller ones and simplify complex operations involving exponents. They have applications in physics, computer science, engineering, and various other areas.

14. What are the 3 types of logarithms?

There are three main types of logarithms:

Common Logarithms (base-10): Represented as log(x), where x is any positive number.

Natural Logarithms (base-e): Represented as ln(x), where e is a mathematical constant (approximately 2.71828).

Logarithms with Any Base (b): Represented as $\log_b(x)$, where b is any positive number and b ≠ 1.