Topic 6: Logarithms with Exercises

What is Logarithms?
A logarithms is a simple given number that be produce which can be raised by representing the the quantity of power to fixed the number. (base)

Basic simple of using the logarithms:

Example 1:
How many 2's do we multiply to get 8?

Answer:
2 x 2 x 2 = 8, so we had to multiply 3 of the 2's to get 8

So, the logarithm is 3

Example 2:
What is Log ₅ 625?
How many 5's is needed to be multiplied together to get 625?
5 x 5 x 5 x 5 = 625, so we need to be 4 of the 5's

Answer:
Log ₅ 625 = 4

Example 3:
What is Log 4 64?How many 2's need to be multiplied together to get 64?
 2 x 2 x 2 x 2 x 2 x 2 = 64, so we need 6 of the 2's

Answer:
Log 4 64 = 6


An Exponents

It's how many times to use the number in multiplications.
Example:8² = 8 x 8 = 64

(2 is used 2 times in a multiplication to get 64)

So if a logarithm answer a question like this:
 2? = 8

so this way,

The logarithm tell us what the exponent is!

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

what exponents that we need?
the general case:

Example 1:
What is  Log ₁₀ 100 ?

10² = 100

So an exponent of 2 is needed to make 10 into 100, and:

Log ₁₀ 100 = 2

Example 2:
What is  Log 3 81 ?
So an exponent of 4 is needed to make 3 into 81 and:

Log 3 81 = 4

Example 3:
What is Log 3 27?
So an exponent of 3 is needed to make 3 into 27 and:

Log 3 27 = 3

HERE IS SOME VIDEO FOR YOUR UNDERSTANDING. 

-EXERCISE-
!GOOD LUCK!


Question 1:
 What is log ₄ 256?

Question 2:
 What is log ₃ 729?

Question 3: 
 Given that 3² = 9 in exponent from, how would you write this in logarithm form?