EXPONENTIAL FORM TO LOGARITHMIC FORM

Converting exponential into logarithmic form : 

x^y = k -----> y = log _x k

Example 1 :

Obtain the equivalent logarithmic form of the following.

 6^-4  =  1/1296

Solution :

Given exponential form :

6^-4  =  1/1296

Logarithmic form :

-4  =  log₆ (1/1296)

Example 2 :

Obtain the equivalent logarithmic form of the following.

 (1/81)^3/4  =  1/27

Solution :

Given exponential form :

 (1/81)^3/4  =  1/27

Logarithmic form :

3/4  =  log_(1/81) (1/27)

Example 3 :

Obtain the equivalent logarithmic form of the following.

 6  =  (216)^1/3

Solution :

Given exponential form :

6  =  (216)^1/3

Logarithmic form :

log₂₁₆ 6  =  1/3

Example 4 :

Obtain the equivalent logarithmic form of the following.

 (13)^-1  =  1/13

Solution :

Given exponential form :

 (13)^-1  =  1/13

Logarithmic form :

-1  =  log₁₃ (1/13)

Example 5 :

Obtain the equivalent logarithmic form of the following.

 1/4  =  8^-2/3

Solution :

Given exponential form :

 1/4  =  8^-2/3

Logarithmic form :

 log₈ (1/4)  =  -2/3

Example 6 :

Obtain the equivalent logarithmic form of the following.

25^1/2  =  5

Solution :

Given exponential form :

25^1/2  =  5

Logarithmic form :

1/2  =  log₂₅ 5

Example 7 :

Obtain the equivalent logarithmic form of the following.

1/144  =  12^-2

Solution :

Given exponential form :

1/144  =  12^-2

Logarithmic form :

log₁₂ (1/144)  =  -2

Example 8 :

Obtain the equivalent logarithmic form of the following.

0.1  =  10^-1 

Solution :

Given exponential form :

0.1  =  10^-1 

Logarithmic form :

log₁₀ (0.1)  =  -1

Example 9 :

Obtain the equivalent logarithmic form of the following.

2⁴  =  16

Solution :

Given exponential form :

2⁴  =  16

Logarithmic form :

4  =  log₂ 16

Example 10 :

Obtain the equivalent logarithmic form of the following.

3⁵  =  243

Solution :

Given exponential form :

3⁵  =  243

Logarithmic form :

5  =  log₃ 243

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