# EXPONENTIAL FORM TO LOGARITHMIC FORM

Converting exponential into logarithmic form :

xy = k -----> y = log 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.

251/2  =  5

Solution :

Given exponential form :

251/2  =  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 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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