CONVERTING BETWEEN LOGARITHMIC AND EXPONENTIAL FORMS

In this section, you will learn the following two conversions. 

(i) Logarithmic to exponential form.

(ii) Exponential to logarithmic form.

Example 1 :

Convert the following to exponential form : 

log₄64  =  3

Solution :

64  =  4³

Example 2 :

Convert the following to exponential form : 

log₅(1/25)  =  -2

Solution :

1/25  =  5^-2

Example 3 :

Convert the following to exponential form : 

log_√39  =  4

Solution :

9  =  (√3)⁴

Example 4 :

Convert the following to exponential form : 

log₁₀0.1 =  -1

Solution :

0.1  =  10^-1

Example 5 :

Convert the following to exponential form : 

log_0.58  =  -3

Solution :

8  =  0.5^-3

Example 6 :

Convert the following to logarithmic form : 

1/1296  =  6^-4

Solution :

log₆(1/1296)  =  -4

Example 7 :

Convert the following to logarithmic form : 

 (1/81)^3/4  =  1/27

Solution :

3/4  =  log_(1/81)(1/27)

Example 8 :

Convert the following to logarithmic form : 

 (13)^-1  =  1/13

Solution :

-1  =  log₁₃(1/13)

Example 9 :

Convert the following to logarithmic form : 

 8^-2/3  =  1/4

Solution :

-2/3  =  log₈(1/4)

Example 10 :

Convert the following to logarithmic form : 

10^-1  =  0.1

Solution :

-1  =  log₁₀(0.1)

Example 11 :

Solve for x :

log₂x  =  1/2

Solution :

log₂x  =  1/2

Convert to exponential form. 

x  =  2^1/2

x  =  √2

Example 12 :

Solve for x :

log_1/5x  =  3

Solution :

log_1/5x  =  3

Convert to exponential form. 

x  =  (1/5)³

x  =  1³/5³

x  =  1/125

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