# EXPONENTIAL FORM TO LOGARITHMIC FORM

## About "Exponential form to logarithmic form"

Exponential form to logarithmic form :

Here we are going to see how to convert exponential form to logarithmic form. Let us look into some examples to understand the concept given above.

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)

log6 (1/1296)  =  -4

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)

log(1/81) (1/27)  =  3/4

Example 3 :

Obtain the equivalent logarithmic form of the following

(216)1/3  =  6

Solution :

Given exponential form :

(216)1/3  =  6

Logarithmic form :

1/3  =  log216 6

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)

log13 (1/13)  =  -1

Example 5 :

Obtain the equivalent logarithmic form of the following

8-2/3  =  1/4

Solution :

Given exponential form :

8-2/3  =  1/4

Logarithmic form :

-2/3  =  log8 (1/4)

log8 (1/4)  =  -2/3

Example 6 :

Obtain the equivalent logarithmic form of the following

251/2  =  5

Solution :

Given exponential form :

251/2  =  5

Logarithmic form :

1/2  =  log25 5

log25 5  =  1/2

Example 7 :

Obtain the equivalent logarithmic form of the following

12-2  =  1/144

Solution :

Given exponential form :

12-2  =  1/144

Logarithmic form :

-2  =  log12 (1/144)

log12 (1/144)  =  -2

Example 8 :

Obtain the equivalent logarithmic form of the following

10-1  =  0.1

Solution :

Given exponential form :

10-1  =  0.1

Logarithmic form :

-1  =  log10 (0.1)

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

log2 16  =  4

Example 10 :

Obtain the equivalent logarithmic form of the following

35  =  243

Solution :

Given exponential form :

35  =  243

Logarithmic form :

5  =  log3 243

log3 243  =  5 After having gone through the stuff given above, we hope that the students would have understood "Exponential form to logarithmic form".

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