TOPIC 4 : LOGARITHMS

What is logarithms?

A logarithm is the power to which a number must be raised in order to get some other number. "opposite" of  exponential just as subtraction is the opposite if addition and division is the opposite of multiplication

log 100 = 2

because,

10² = 100

Example 1:

Solve for x in the equation 7Log(3x)=15.

Solution:

Step 1: Isolate the logarithmic term before you convert the logarithmic equation to an exponential equation. Divide both sides of the original equation by 7:

Step 2: Convert the logarithmic equation to an exponential equation: If no base is indicated, it means the base of the logarithm is 10. Recall also that logarithms are exponents,

 so the exponent is  

   

The equation

can now be written

Example 2: 

What is log2 (64)??

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

Solution:

2 x 2 x 2 x 2 x 2 x 2 = 64, so we need 6 of the 2s

Log 2 (64) = 6

Question!

Log₄ (16) = 2

Log₈ (x) = 2

Log₈ (64) = x

Example 3: 

What Is log₅(625)?

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

Answer: log₅(625) = 4 

QUESTIONS for Logarithms.

1. Which of the following statements is not correct?

A.            log 10 10 = 1

B.            log (2 + 3) = log (2 x 3)

C.            log 10 1 = 0

D.            log (1 + 2 + 3) = log 1 + log 2 + log 3

2. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

A.            2.870

B.            2.967

C.            3.876

D.            3.912

3. If log 27 = 1.431, then the value of log 9 is:

A.            0.934

B.            0.945

C.            0.954

D.            0.958