TOPIC 2 : LOGARITHMS

What Is Logarithms?

• A logarithm is the power to which a number must be raised in order to get some other number.  

For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100 :

log 100 = 2 it is because 10² = 100

Second example - What Is log₅(625)?

5 × 5 × 5 × 5 = 625, so we need 4 of the 5s.

Answer: log₅(625) = 4

Third example -  What is log₂(64)?

We are asking "how many 2s need to be multiplied together to get 64?

2 × 2 × 2 × 2 × 2 × 2 = 64, so we need 6 of the 2s.

Answer: log₂(64) = 6

➛ EXPONENTS AND LOGARITHMS ARE RELATED

             

The exponent says how many times to use the number in a multiplication.

In this example: 2³ = 2 × 2 × 2 = 8

(2 is used 3 times in a multiplication to get 8)

So a logarithm answers a question like this:

 In this way ↣

The logarithm tells us what the exponent is.


In that example the "base" is 2 and the "exponent" is 3:

 QUESTIONS ↷

1. What is log₃(729)?
2.  What is log₄(256)?

REMEMBER THE LOGARITHM LAWS❗